Theorem 3adant1r 1234

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 1207	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1202	1 |- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 981

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 983

This theorem is referenced by:  3adant2r  1236  3adant3r  1238  tfr1onlembacc  6451  tfr1onlembfn  6453  tfr1onlemaccex  6457  tfr1onlemres  6458  tfrcllembfn  6466  tfrcllemaccex  6470  tfrcllemres  6471  tfrcldm  6472  tfrcl  6473  mulassnqg  7532  prarloc  7651  prmuloc  7714  addasssrg  7904  axaddass  8020  ghmgrp  13569