Theorem 3adant3r3 1216

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)

Hypothesis

Ref	Expression
3exp.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant3r3	|- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )

Proof of Theorem 3adant3r3

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expb 1206	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr3 1160	1 |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  grpaddsubass  13165  grpsubsub4  13168  grpnpncan  13170  imasgrp2  13183  imasgrp  13184  cmn12  13379  abladdsub  13388  imasrng  13455  imasring  13563  opprrng  13576  opprring  13578  dvrass  13638  lss1  13861  mettri2  14541  xmetrtri  14555