Theorem ax16ALT 1273

Description: Version of ax16 1211 that doesn't require ax-10 968 or ax-12 970 for its proof.

Assertion

Ref	Expression
ax16ALT	|- (A.x x = y -> (ph -> A.xph))

Distinct variable group:   x,y

Proof of Theorem ax16ALT

Step	Hyp	Ref	Expression
1		sbequ12 1183	. 2 |- (x = z -> (ph <-> [z / x]ph))
2		ax-17 973	. . 3 |- (ph -> A.zph)
3	2	hbsb3 1208	. 2 |- ([z / x]ph -> A.x[z / x]ph)
4	1, 3	ax16i 1272	1 |- (A.x x = y -> (ph -> A.xph))

Syntax hints:   -> wi 3  A.wal 956   = wceq 958  [wsbc 1172

This theorem is referenced by:  dvelimALT 1355

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-9 967  ax-11 969  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174

Copyright terms: Public domain