Theorem 3adant3r1 1215

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 1207	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr1 1159	1 |- ( ( ph /\ ( ta /\ ps /\ 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:  ccatswrd  11123  imasmnd2  13284  grpsubsub  13421  grpnnncan2  13429  imasgrp2  13446  mulgnn0ass  13494  mulgsubdir  13498  cmn32  13640  ablsubadd  13648  imasrng  13718  imasring  13826  opprrng  13839  opprring  13841  xmettri3  14846  mettri3  14847  xmetrtri  14848  rprelogbmulexp  15428