Theorem eel3132 38940

Description: syl2an 494 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.)

Hypotheses

Ref	Expression
eel3132.1	|- ( ( ph /\ ps ) -> ch )
eel3132.2	|- ( ( th /\ ps ) -> ta )
eel3132.3	|- ( ( ch /\ ta ) -> et )

Assertion

Ref	Expression
eel3132	|- ( ( ph /\ th /\ ps ) -> et )

Proof of Theorem eel3132

Step	Hyp	Ref	Expression
1		eel3132.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2		eel3132.2	. . 3 |- ( ( th /\ ps ) -> ta )
3		eel3132.3	. . 3 |- ( ( ch /\ ta ) -> et )
4	1, 2, 3	syl2an 494	. 2 |- ( ( ( ph /\ ps ) /\ ( th /\ ps ) ) -> et )
5	4	3impdir 1382	1 |- ( ( ph /\ th /\ ps ) -> et )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

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)