Theorem dvelimf 1250

Description: Version of dvelim 1352 without any variable restrictions.

Hypotheses

Ref	Expression
dvelimf.1	|- (ph -> A.xph)
dvelimf.2	|- (ps -> A.zps)
dvelimf.3	|- (z = y -> (ph <-> ps))

Assertion

Ref	Expression
dvelimf	|- (-. A.x x = y -> (ps -> A.xps))

Proof of Theorem dvelimf

Step	Hyp	Ref	Expression
1		dvelimf.1	. . 3 |- (ph -> A.xph)
2	1	hbsb4 1248	. 2 |- (-. A.x x = y -> ([y / z]ph -> A.x[y / z]ph))
3		dvelimf.2	. . 3 |- (ps -> A.zps)
4		dvelimf.3	. . 3 |- (z = y -> (ph <-> ps))
5	3, 4	sbie 1196	. 2 |- ([y / z]ph <-> ps)
6	5	albii 999	. 2 |- (A.x[y / z]ph <-> A.xps)
7	2, 5, 6	3imtr3g 552	1 |- (-. A.x x = y -> (ps -> A.xps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146  A.wal 954   = wceq 956

This theorem is referenced by:  dvelim 1352

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-11o 1218

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

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