Theorem 3adant1l 1174

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
3adant1l	|- (((ta /\ ph) /\ ps /\ ch) -> th)

Proof of Theorem 3adant1l

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3expb 1152	. . 3 |- ((ph /\ (ps /\ ch)) -> th)
3	2	adantll 694	. 2 |- (((ta /\ ph) /\ (ps /\ ch)) -> th)
4	3	3impb 1147	1 |- (((ta /\ ph) /\ 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:  3adant2l  1176  3adant3l  1178