Theorem 3ad2antl2 1162

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

Hypothesis

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

Assertion

Ref	Expression
3ad2antl2	|- ( ( ( ps /\ ph /\ ta ) /\ ch ) -> th )

Proof of Theorem 3ad2antl2

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ch ) -> th )
3	2	3adantl1 1155	1 |- ( ( ( ps /\ ph /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  fcofo  5827  cocan1  5830  acexmid  5917  caovimo  6112  ordiso2  7094  mkvprop  7217  ltpopr  7655  ltsopr  7656  addcanprleml  7674  addcanprlemu  7675  aptiprlemu  7700  seq1g  10534  dvdsmodexp  11938  muldvds1  11959  lcmdvds  12217  cnpnei  14387