Theorem a16gb 1819

Description: A generalization of axiom ax-16 1768. (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 1818	. 2 |- ( A. x x = y -> ( ph -> A. z ph ) )
2		ax-4 1470	. 2 |- ( A. z ph -> ph )
3	1, 2	impbid1 141	1 |- ( A. x x = y -> ( ph <-> A. z ph ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1312

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497

This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719

This theorem is referenced by: (None)