Theorem a4imed 1163

Description: Deduction version of a4ime 1162.

Hypotheses

Ref	Expression
a4imed.1	|- (ch -> A.xch)
a4imed.2	|- (ch -> (ph -> A.xph))
a4imed.3	|- (x = y -> (ph -> ps))

Assertion

Ref	Expression
a4imed	|- (ch -> (ph -> E.xps))

Proof of Theorem a4imed

Step	Hyp	Ref	Expression
1		a4imed.1	. . . . . 6 |- (ch -> A.xch)
2	1	adantr 391	. . . . 5 |- ((ch /\ ph) -> A.xch)
3		a4imed.2	. . . . . 6 |- (ch -> (ph -> A.xph))
4	3	imp 350	. . . . 5 |- ((ch /\ ph) -> A.xph)
5	2, 4	jca 288	. . . 4 |- ((ch /\ ph) -> (A.xch /\ A.xph))
6		19.26 1069	. . . 4 |- (A.x(ch /\ ph) <-> (A.xch /\ A.xph))
7	5, 6	sylibr 200	. . 3 |- ((ch /\ ph) -> A.x(ch /\ ph))
8		a4imed.3	. . . 4 |- (x = y -> (ph -> ps))
9	8	adantld 392	. . 3 |- (x = y -> ((ch /\ ph) -> ps))
10	7, 9	a4ime 1162	. 2 |- ((ch /\ ph) -> E.xps)
11	10	ex 373	1 |- (ch -> (ph -> E.xps))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 956   = wceq 958  E.wex 982

This theorem is referenced by:  equvini 1170

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

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