Theorem 3adantr1 1114

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Hypothesis

Ref	Expression
3adantr.1	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
3adantr1	|- ((ph /\ (ta /\ ps /\ ch)) -> th)

Proof of Theorem 3adantr1

Step	Hyp	Ref	Expression
1		3simpc 954	. 2 |- ((ta /\ ps /\ ch) -> (ps /\ ch))
2		3adantr.1	. 2 |- ((ph /\ (ps /\ ch)) -> th)
3	1, 2	sylan2 460	1 |- ((ph /\ (ta /\ ps /\ ch)) -> th)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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  df-3an 936

This theorem is referenced by:  3ad2antr3  1122  3adant3r1  1160  nnsucelr  4429