Theorem ax16ALT 1271

Description: Version of ax16 1209 that doesn't require ax-10 966 or ax-12 968 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 1181	. 2 |- (x = z -> (ph <-> [z / x]ph))
2		ax-17 971	. . 3 |- (ph -> A.zph)
3	2	hbsb3 1206	. 2 |- ([z / x]ph -> A.x[z / x]ph)
4	1, 3	ax16i 1270	1 |- (A.x x = y -> (ph -> A.xph))

Syntax hints:   -> wi 3  A.wal 954   = wceq 956  [wsbc 1170

This theorem is referenced by:  dvelimALT 1353

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-9 965  ax-11 967  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172

Copyright terms: Public domain