Theorem eel1111 38947

Description: Four-hypothesis elimination deduction for an assertion with a singleton virtual hypothesis collection. Similar to syl112anc 1330 except the unification theorem uses left-nested conjunction. (Contributed by Alan Sare, 17-Oct-2017.)

Hypotheses

Ref	Expression
eel1111.1	|- ( ph -> ps )
eel1111.2	|- ( ph -> ch )
eel1111.3	|- ( ph -> th )
eel1111.4	|- ( ph -> ta )
eel1111.5	|- ( ( ( ( ps /\ ch ) /\ th ) /\ ta ) -> et )

Assertion

Ref	Expression
eel1111	|- ( ph -> et )

Proof of Theorem eel1111

Step	Hyp	Ref	Expression
1		eel1111.4	. 2 |- ( ph -> ta )
2		eel1111.1	. . 3 |- ( ph -> ps )
3		eel1111.2	. . 3 |- ( ph -> ch )
4		eel1111.3	. . 3 |- ( ph -> th )
5		eel1111.5	. . . 4 |- ( ( ( ( ps /\ ch ) /\ th ) /\ ta ) -> et )
6	5	exp41 638	. . 3 |- ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) )
7	2, 3, 4, 6	syl3c 66	. 2 |- ( ph -> ( ta -> et ) )
8	1, 7	mpd 15	1 |- ( ph -> et )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  sineq0ALT  39173