Theorem 3adant3r1 1243

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 1235	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr1 1187	1 |- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  ccatswrd  11456  imasmnd2  13808  grpsubsub  13943  grpnnncan2  13951  imasgrp2  13962  mulgnn0ass  14010  mulgsubdir  14014  cmn32  14156  ablsubadd  14165  imasrng  14304  imasring  14418  opprrng  14431  opprring  14433  xmettri3  15524  mettri3  15525  xmetrtri  15526  rprelogbmulexp  16111