Theorem adantrll 758

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)

Hypothesis

Ref	Expression
adantr2.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Assertion

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

Proof of Theorem adantrll

Step	Hyp	Ref	Expression
1		simpr 477	. 2 |- ( ( ta /\ ps ) -> ps )
2		adantr2.1	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	1, 2	sylanr1 684	1 |- ( ( ph /\ ( ( ta /\ ps ) /\ ch ) ) -> th )

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:  lo1le  14382  nrmmetd  22379  mdslmd3i  29191