Theorem ad2antlr 707

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999.) (Proof shortened by Wolf Lammen, 20-Nov-2012.)

Hypothesis

Ref	Expression
ad2ant.1	|- (ph -> ps)

Assertion

Ref	Expression
ad2antlr	|- (((ch /\ ph) /\ th) -> ps)

Proof of Theorem ad2antlr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- (ph -> ps)
2	1	adantr 451	. 2 |- ((ph /\ th) -> ps)
3	2	adantll 694	1 |- (((ch /\ ph) /\ th) -> ps)

Syntax hints:   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  ad3antlr  711  simplr  731  simplrl  736  simplrr  737  ax11eq  2193  ax11el  2194  ltfinirr  4458  sfintfin  4533  caovord3  5632  nntccl  6171  sbthlem3  6206  nchoicelem17  6306