Theorem 3adant1l 1209

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 1183	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantll 468	. 2 |- ( ( ( ta /\ ph ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1178	1 |- ( ( ( ta /\ ph ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 963

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

This theorem depends on definitions:  df-bi 116  df-3an 965

This theorem is referenced by:  3adant2l  1211  3adant3l  1213  tfrcl  6269  addassnqg  7214  mulassnqg  7216  addasssrg  7588  axaddass  7704