Theorem 3adant3r1 1236

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 1228	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr1 1180	1 |- ( ( ph /\ ( ta /\ ps /\ 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:  ccatswrd  11218  imasmnd2  13501  grpsubsub  13638  grpnnncan2  13646  imasgrp2  13663  mulgnn0ass  13711  mulgsubdir  13715  cmn32  13857  ablsubadd  13865  imasrng  13935  imasring  14043  opprrng  14056  opprring  14058  xmettri3  15064  mettri3  15065  xmetrtri  15066  rprelogbmulexp  15646