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Metamath Proof Explorer

Theorem 19.42v

Description: Version of 19.42 with a disjoint variable condition requiring fewer axioms. (Contributed by NM, 21-Jun-1993)

Ref Expression
Assertion 19.42v 
|- ( E. x ( ph /\ ps ) <-> ( ph /\ E. x ps ) )

Proof

Step Hyp Ref Expression
1 19.41v 
 |-  ( E. x ( ps /\ ph ) <-> ( E. x ps /\ ph ) )
2 exancom 
 |-  ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) )
3 ancom 
 |-  ( ( ph /\ E. x ps ) <-> ( E. x ps /\ ph ) )
4 1 2 3 3bitr4i 
 |-  ( E. x ( ph /\ ps ) <-> ( ph /\ E. x ps ) )