Theorem dveeq1ALT 1355

Description: Version of dveeq1 1354 using ax-16 1210 instead of ax-17 971.

Assertion

Ref	Expression
dveeq1ALT	|- (-. A.x x = y -> (y = z -> A.x y = z))

Distinct variable group:   x,z

Proof of Theorem dveeq1ALT

Step	Hyp	Ref	Expression
1		ax17eq 1211	. 2 |- (w = z -> A.x w = z)
2		ax17eq 1211	. 2 |- (y = z -> A.w y = z)
3		equequ1 1134	. 2 |- (w = y -> (w = z <-> y = z))
4	1, 2, 3	dvelimfALT 1153	1 |- (-. A.x x = y -> (y = z -> A.x y = z))

Syntax hints:  -. wn 2   -> wi 3  A.wal 954   = wceq 956

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-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210

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

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