Theorem a16gb 1272

Description: A generalization of axiom ax-16 1206.

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 1271	. 2 |- (A.x x = y -> (ph -> A.zph))
2		ax-4 970	. 2 |- (A.zph -> ph)
3	1, 2	impbid1 515	1 |- (A.x x = y -> (ph <-> A.zph))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 951   = wceq 953

This theorem is referenced by:  sbal 1342

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-9 962  ax-10 963  ax-12 965  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206

This theorem depends on definitions:  df-bi 147  df-an 225

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