Theorem a16gb 1786

Description: A generalization of axiom ax-16 1735. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
a16gb	|- ( A. x x = y -> ( ph <-> A. z ph ) )

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y, z)

Proof of Theorem a16gb

Step	Hyp	Ref	Expression
1		a16g 1785	. 2 |- ( A. x x = y -> ( ph -> A. z ph ) )
2		ax-4 1440	. 2 |- ( A. z ph -> ph )
3	1, 2	impbid1 140	1 |- ( A. x x = y -> ( ph <-> A. z ph ) )

Syntax hints:   -> wi 4   <-> wb 103   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686

This theorem is referenced by: (None)