Theorem ad3antrrr 710

Description: Deduction adding three conjuncts to antecedent. (Contributed by NM, 28-Jul-2012.)

Hypothesis

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

Assertion

Ref	Expression
ad3antrrr	|- ((((ph /\ ch) /\ th) /\ ta) -> ps)

Proof of Theorem ad3antrrr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 |- (ph -> ps)
2	1	adantr 451	. 2 |- ((ph /\ ch) -> ps)
3	2	ad2antrr 706	1 |- ((((ph /\ ch) /\ th) /\ ta) -> 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:  ad4antr  712  ncfinraise  4482