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  13759  imasmnd  13760  grpaddsubass  13895  grpsubsub4  13898  grpnpncan  13900  imasgrp2  13913  imasgrp  13914  cmn12  14109  abladdsub  14119  imasrng  14255  imasring  14369  opprrng  14382  opprring  14384  dvrass  14446  lss1  14699  mettri2  15463  xmetrtri  15477