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  6427  tfr1onlembfn  6429  tfr1onlemaccex  6433  tfr1onlemres  6434  tfrcllembfn  6442  tfrcllemaccex  6446  tfrcllemres  6447  tfrcldm  6448  tfrcl  6449  mulassnqg  7496  prarloc  7615  prmuloc  7678  addasssrg  7868  axaddass  7984  ghmgrp  13425