Theorem adantlll 477

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 2-Dec-2012.)

Hypothesis

Ref	Expression
adantl2.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )

Assertion

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

Proof of Theorem adantlll

Step	Hyp	Ref	Expression
1		simpr 109	. 2 |- ( ( ta /\ ph ) -> ph )
2		adantl2.1	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	1, 2	sylanl1 400	1 |- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103

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 is referenced by:  ad4ant23  512  ad4ant24  513  ad4ant234  1213  fun11iun  5463  fiintim  6906  cnegexlem3  8096  bezoutlemzz  11957  cnptopco  13016