bnj591

Description: Technical lemma for bnj852 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	bnj591.1	No typesetting found for \|- ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode \|-
	Assertion	bnj591	Could not format assertion : No typesetting found for \|- ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode \|-

Proof

Step	Hyp	Ref	Expression
1		bnj591.1	Could not format ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for \|- ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode \|-
2	1	sbcbii	Could not format ( [. k / j ]. th <-> [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for \|- ( [. k / j ]. th <-> [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode \|-
3		vex	$⊢ k \in V$
4		fveq2	$⊢ j = k \to f (j) = f (k)$
5		fveq2	$⊢ j = k \to g (j) = g (k)$
6	4 5	eqeq12d	$⊢ j = k \to (f (j) = g (j) \leftrightarrow f (k) = g (k))$
7	6	imbi2d	Could not format ( j = k -> ( ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) ) : No typesetting found for \|- ( j = k -> ( ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) ) with typecode \|-
8	3 7	sbcie	Could not format ( [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) : No typesetting found for \|- ( [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode \|-
9	2 8	bitri	Could not format ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) : No typesetting found for \|- ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode \|-

Metamath Proof Explorer

Theorem bnj591

Proof