Theorem 3adant1r 1233

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 1206	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1201	1 |- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 982

This theorem is referenced by:  3adant2r  1235  3adant3r  1237  tfr1onlembacc  6409  tfr1onlembfn  6411  tfr1onlemaccex  6415  tfr1onlemres  6416  tfrcllembfn  6424  tfrcllemaccex  6428  tfrcllemres  6429  tfrcldm  6430  tfrcl  6431  mulassnqg  7468  prarloc  7587  prmuloc  7650  addasssrg  7840  axaddass  7956  ghmgrp  13324