Theorem eel2131 28896

Description: syl2an 465 with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016.)

Hypotheses

Ref	Expression
eel2131.1	|- ( ( ph /\ ps ) -> ch )
eel2131.2	|- ( ( ph /\ th ) -> ta )
eel2131.3	|- ( ( ch /\ ta ) -> et )

Assertion

Ref	Expression
eel2131	|- ( ( ph /\ ps /\ th ) -> et )

Proof of Theorem eel2131

Step	Hyp	Ref	Expression
1		eel2131.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2		eel2131.2	. . 3 |- ( ( ph /\ th ) -> ta )
3		eel2131.3	. . 3 |- ( ( ch /\ ta ) -> et )
4	1, 2, 3	syl2an 465	. 2 |- ( ( ( ph /\ ps ) /\ ( ph /\ th ) ) -> et )
5	4	3impdi 1240	1 |- ( ( ph /\ ps /\ th ) -> et )

Syntax hints:   -> wi 4   /\ wa 360   /\ w3a 937

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 179  df-an 362  df-3an 939