Theorem dveeq1 1353

Description: Quantifier introduction when one pair of variables is distinct.

Assertion

Ref	Expression
dveeq1	|- (-. A.x x = y -> (y = z -> A.x y = z))

Distinct variable group:   x,z

Proof of Theorem dveeq1

Step	Hyp	Ref	Expression
1		ax-17 970	. 2 |- (w = z -> A.x w = z)
2		ax-17 970	. 2 |- (y = z -> A.w y = z)
3		equequ1 1133	. 2 |- (w = y -> (w = z <-> y = z))
4	1, 2, 3	dvelimfALT 1152	1 |- (-. A.x x = y -> (y = z -> A.x y = z))

Syntax hints:  -. wn 2   -> wi 3  A.wal 953   = wceq 955

This theorem is referenced by:  sbal2 1357  ax11inda2ALT 1368  hbeu 1388  dfid3 2832  axpowndlem4 4935

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139

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

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