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  11126  imasmnd2  13317  grpsubsub  13454  grpnnncan2  13462  imasgrp2  13479  mulgnn0ass  13527  mulgsubdir  13531  cmn32  13673  ablsubadd  13681  imasrng  13751  imasring  13859  opprrng  13872  opprring  13874  xmettri3  14879  mettri3  14880  xmetrtri  14881  rprelogbmulexp  15461