Theorem 3adant3r1 1238

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 1230	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr1 1182	1 |- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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 1006

This theorem is referenced by:  ccatswrd  11255  imasmnd2  13553  grpsubsub  13690  grpnnncan2  13698  imasgrp2  13715  mulgnn0ass  13763  mulgsubdir  13767  cmn32  13909  ablsubadd  13917  imasrng  13988  imasring  14096  opprrng  14109  opprring  14111  xmettri3  15117  mettri3  15118  xmetrtri  15119  rprelogbmulexp  15699