Theorem 3adant2l 1263

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 1238	. . 3 |- ( ( ps /\ ph /\ ch ) -> th )
3	2	3adant1l 1261	. 2 |- ( ( ( ta /\ ps ) /\ ph /\ ch ) -> th )
4	3	3com12 1238	1 |- ( ( ph /\ ( ta /\ ps ) /\ ch ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  sbthlemi4  7277  addassnqg  7749  mulassnqg  7751  prmuloc  7933  ltpopr  7962  addasssrg  8123  axaddass  8239