Theorem 3adant3r3 1217

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 1207	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr3 1161	1 |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> 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:  imasmnd2  13284  imasmnd  13285  grpaddsubass  13422  grpsubsub4  13425  grpnpncan  13427  imasgrp2  13446  imasgrp  13447  cmn12  13642  abladdsub  13651  imasrng  13718  imasring  13826  opprrng  13839  opprring  13841  dvrass  13901  lss1  14124  mettri2  14834  xmetrtri  14848