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  5853  cocan1  5856  acexmid  5943  caovimo  6140  ordiso2  7137  mkvprop  7260  ltpopr  7708  ltsopr  7709  addcanprleml  7727  addcanprlemu  7728  aptiprlemu  7753  seq1g  10608  dvdsmodexp  12106  muldvds1  12127  lcmdvds  12401  cnpnei  14691