Theorem 3adant3r1 1214

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)

Hypothesis

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

Assertion

Ref	Expression
3adant3r1	|- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )

Proof of Theorem 3adant3r1

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expb 1206	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr1 1158	1 |- ( ( ph /\ ( ta /\ ps /\ 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:  imasmnd2  13154  grpsubsub  13291  grpnnncan2  13299  imasgrp2  13316  mulgnn0ass  13364  mulgsubdir  13368  cmn32  13510  ablsubadd  13518  imasrng  13588  imasring  13696  opprrng  13709  opprring  13711  xmettri3  14694  mettri3  14695  xmetrtri  14696  rprelogbmulexp  15276