Theorem spimed 1625

Description: Deduction version of spime 1626. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 19-Feb-2018.)

Hypotheses

Ref	Expression
spimed.1	|- (ch -> F/xph)
spimed.2	|- (x = y -> (ph -> ps))

Assertion

Ref	Expression
spimed	|- (ch -> (ph -> E.xps))

Proof of Theorem spimed

Step	Hyp	Ref	Expression
1		spimed.1	. . 3 |- (ch -> F/xph)
2	1	nfrd 1410	. 2 |- (ch -> (ph -> A.xph))
3		a9e 1583	. . . 4 |- E.x x = y
4		spimed.2	. . . 4 |- (x = y -> (ph -> ps))
5	3, 4	eximii 1490	. . 3 |- E.x(ph -> ps)
6	5	19.35i 1513	. 2 |- (A.xph -> E.xps)
7	2, 6	syl6 29	1 |- (ch -> (ph -> E.xps))

Syntax hints:   -> wi 4  A.wal 1240   F/wnf 1346  E.wex 1378

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-i9 1420  ax-ial 1424

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  spime  1626