Theorem spimed 1977

Description: Deduction version of spime 1976. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.)

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	. 2 |- (ch -> F/xph)
2		nfnf1 1790	. . . . 5 |- F/x F/xph
3		id 19	. . . . 5 |- ( F/xph -> F/xph)
4	2, 3	nfan1 1881	. . . 4 |- F/x( F/xph /\ ph)
5		spimed.2	. . . . 5 |- (x = y -> (ph -> ps))
6	5	adantld 453	. . . 4 |- (x = y -> (( F/xph /\ ph) -> ps))
7	4, 6	spime 1976	. . 3 |- (( F/xph /\ ph) -> E.xps)
8	7	ex 423	. 2 |- ( F/xph -> (ph -> E.xps))
9	1, 8	syl 15	1 |- (ch -> (ph -> E.xps))

Syntax hints:   -> wi 4   /\ wa 358  E.wex 1541   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  equvini  1987