Theorem eel000cT 38928

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eel000cT.1	|- ph
eel000cT.2	|- ps
eel000cT.3	|- ch
eel000cT.4	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
eel000cT	|- ( T. -> th )

Proof of Theorem eel000cT

Step	Hyp	Ref	Expression
1		eel000cT.3	. . 3 |- ch
2		eel000cT.2	. . . 4 |- ps
3		eel000cT.1	. . . . 5 |- ph
4		eel000cT.4	. . . . 5 |- ( ( ph /\ ps /\ ch ) -> th )
5	3, 4	mp3an1 1411	. . . 4 |- ( ( ps /\ ch ) -> th )
6	2, 5	mpan 706	. . 3 |- ( ch -> th )
7	1, 6	ax-mp 5	. 2 |- th
8	7	a1i 11	1 |- ( T. -> th )

Syntax hints:   -> wi 4   /\ w3a 1037   T. wtru 1484

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  df-3an 1039

This theorem is referenced by: (None)