Theorem 3ad2antl2 1184

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 1177	1 |- ( ( ( ps /\ ph /\ ta ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  fcofo  5908  cocan1  5911  acexmid  6000  caovimo  6199  ordiso2  7202  mkvprop  7325  ltpopr  7782  ltsopr  7783  addcanprleml  7801  addcanprlemu  7802  aptiprlemu  7827  seq1g  10685  dvdsmodexp  12306  muldvds1  12327  lcmdvds  12601  cnpnei  14893  upgrpredgv  15944