Theorem 3adant3r3 1238

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 1228	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr3 1182	1 |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> 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:  imasmnd2  13525  imasmnd  13526  grpaddsubass  13663  grpsubsub4  13666  grpnpncan  13668  imasgrp2  13687  imasgrp  13688  cmn12  13883  abladdsub  13892  imasrng  13959  imasring  14067  opprrng  14080  opprring  14082  dvrass  14143  lss1  14366  mettri2  15076  xmetrtri  15090