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  5806  cocan1  5809  acexmid  5895  caovimo  6090  ordiso2  7064  mkvprop  7186  ltpopr  7624  ltsopr  7625  addcanprleml  7643  addcanprlemu  7644  aptiprlemu  7669  dvdsmodexp  11834  muldvds1  11855  lcmdvds  12111  cnpnei  14176