Theorem a16gb 1655

Description: A generalization of axiom ax-16 1580.

Assertion

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

Distinct variable group:   x,y

Proof of Theorem a16gb

Step	Hyp	Ref	Expression
1		a16g 1653	. 2 |- (A.x x = y -> (ph -> A.zph))
2		ax-4 1319	. 2 |- (A.zph -> ph)
3	1, 2	impbid1 575	1 |- (A.x x = y -> (ph <-> A.zph))

Syntax hints:   -> wi 3   <-> wb 163  A.wal 1296   = wceq 1298

This theorem is referenced by:  sbal 1738

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580

This theorem depends on definitions:  df-bi 164  df-an 242

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