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Metamath Proof Explorer

Theorem bnj523

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
Hypotheses bnj523.1 ⊢ φ ↔ F ⁡ ∅ = pred X A R
bnj523.2 No typesetting found for |- ( ph' <-> [. M / n ]. ph ) with typecode |-
bnj523.3 ⊢ M ∈ V
Assertion bnj523 Could not format assertion : No typesetting found for |- ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 bnj523.1 ⊢ φ ↔ F ⁡ ∅ = pred X A R
2 bnj523.2 Could not format ( ph' <-> [. M / n ]. ph ) : No typesetting found for |- ( ph' <-> [. M / n ]. ph ) with typecode |-
3 bnj523.3 ⊢ M ∈ V
4 1 sbcbii ⊢ [˙M / n]˙ φ ↔ [˙M / n]˙ F ⁡ ∅ = pred X A R
5 3 bnj525 ⊢ [˙M / n]˙ F ⁡ ∅ = pred X A R ↔ F ⁡ ∅ = pred X A R
6 2 4 5 3bitri Could not format ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) : No typesetting found for |- ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) with typecode |-