Theorem 3ad2antl3 1192

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 480	. 2 |- ( ( ( ta /\ ph ) /\ ch ) -> th )
3	2	3adantl1 1184	1 |- ( ( ( ps /\ ta /\ ph ) /\ 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:  rspc3ev  2947  brcogw  4949  cocan1  5993  ov6g  6227  prarloclemarch2  7786  ltpopr  7962  ltsopr  7963  zdivmul  9736  lcmdvds  12857