Theorem 3ad2antl2 1163

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 1156	1 |- ( ( ( ps /\ ph /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

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 983

This theorem is referenced by:  fcofo  5876  cocan1  5879  acexmid  5966  caovimo  6163  ordiso2  7163  mkvprop  7286  ltpopr  7743  ltsopr  7744  addcanprleml  7762  addcanprlemu  7763  aptiprlemu  7788  seq1g  10645  dvdsmodexp  12221  muldvds1  12242  lcmdvds  12516  cnpnei  14806  upgrpredgv  15850