Theorem 3adant2l 1129

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
3adant2l	|- ( ( ph /\ ( ta /\ ps ) /\ ch ) -> th )

Proof of Theorem 3adant2l

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3com12 1108	. . 3 |- ( ( ps /\ ph /\ ch ) -> th )
3	2	3adant1l 1127	. 2 |- ( ( ( ta /\ ps ) /\ ph /\ ch ) -> th )
4	3	3com12 1108	1 |- ( ( ph /\ ( ta /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  addassnqg  6480  mulassnqg  6482  prmuloc  6664  ltpopr  6693  addasssrg  6841  axaddass  6946