Theorem adantl3r 509

Description: Deduction adding 1 conjunct to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)

Hypothesis

Ref	Expression
adantl3r.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
adantl3r	|- ( ( ( ( ( ph /\ et ) /\ ps ) /\ ch ) /\ th ) -> ta )

Proof of Theorem adantl3r

Step	Hyp	Ref	Expression
1		id 19	. . 3 |- ( ( ph /\ ps ) -> ( ph /\ ps ) )
2	1	adantlr 474	. 2 |- ( ( ( ph /\ et ) /\ ps ) -> ( ph /\ ps ) )
3		adantl3r.1	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
4	2, 3	sylanl1 400	1 |- ( ( ( ( ( ph /\ et ) /\ ps ) /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  adantl4r  514