Theorem 3adant3r3 1245

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 1235	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr3 1189	1 |- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> 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:  imasmnd2  13808  imasmnd  13809  grpaddsubass  13944  grpsubsub4  13947  grpnpncan  13949  imasgrp2  13962  imasgrp  13963  cmn12  14158  abladdsub  14168  imasrng  14304  imasring  14418  opprrng  14431  opprring  14433  dvrass  14495  lss1  14748  mettri2  15512  xmetrtri  15526