Theorem dveeq2ALT 1215

Description: Version of dveeq2 1214 using ax-16 1212 instead of ax-17 973.

Assertion

Ref	Expression
dveeq2ALT	|- (-. A.x x = y -> (z = y -> A.x z = y))

Distinct variable group:   x,z

Proof of Theorem dveeq2ALT

Step	Hyp	Ref	Expression
1		ax17eq 1213	. 2 |- (z = w -> A.x z = w)
2		ax17eq 1213	. 2 |- (z = y -> A.w z = y)
3		equequ2 1137	. 2 |- (w = y -> (z = w <-> z = y))
4	1, 2, 3	dvelimfALT 1155	1 |- (-. A.x x = y -> (z = y -> A.x z = y))

Syntax hints:  -. wn 2   -> wi 3  A.wal 956   = wceq 958

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-10 968  ax-12 970  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212

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

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