Theorem 3ad2antl3 1161

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antl3	|- ( ( ( ps /\ ta /\ ph ) /\ ch ) -> th )

Proof of Theorem 3ad2antl3

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantll 476	. 2 |- ( ( ( ta /\ ph ) /\ ch ) -> th )
3	2	3adantl1 1153	1 |- ( ( ( ps /\ ta /\ ph ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 980

This theorem is referenced by:  rspc3ev  2858  brcogw  4791  cocan1  5781  ov6g  6005  prarloclemarch2  7396  ltpopr  7572  ltsopr  7573  zdivmul  9319  lcmdvds  12049