Theorem 3adant1l 1167

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 1145	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantll 461	. 2 |- ( ( ( ta /\ ph ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1140	1 |- ( ( ( ta /\ ph ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 925

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 927

This theorem is referenced by:  3adant2l  1169  3adant3l  1171  tfrcl  6143  addassnqg  7002  mulassnqg  7004  addasssrg  7363  axaddass  7468