Theorem 3adant1r 1231

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant1r	|- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Proof of Theorem 3adant1r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expb 1204	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1199	1 |- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

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 980

This theorem is referenced by:  3adant2r  1233  3adant3r  1235  tfr1onlembacc  6342  tfr1onlembfn  6344  tfr1onlemaccex  6348  tfr1onlemres  6349  tfrcllembfn  6357  tfrcllemaccex  6361  tfrcllemres  6362  tfrcldm  6363  tfrcl  6364  mulassnqg  7382  prarloc  7501  prmuloc  7564  addasssrg  7754  axaddass  7870  ghmgrp  12936