Theorem adantrrl 704

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
adantrrl	|- ((ph /\ (ps /\ (ta /\ ch))) -> th)

Proof of Theorem adantrrl

Step	Hyp	Ref	Expression
1		simpr 447	. 2 |- ((ta /\ ch) -> ch)
2		adantr2.1	. 2 |- ((ph /\ (ps /\ ch)) -> th)
3	1, 2	sylanr2 634	1 |- ((ph /\ (ps /\ (ta /\ ch))) -> th)

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: (None)