Theorem 3adant1r 1255

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 1228	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantlr 477	. 2 |- ( ( ( ph /\ ta ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1223	1 |- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  3adant2r  1257  3adant3r  1259  tfr1onlembacc  6488  tfr1onlembfn  6490  tfr1onlemaccex  6494  tfr1onlemres  6495  tfrcllembfn  6503  tfrcllemaccex  6507  tfrcllemres  6508  tfrcldm  6509  tfrcl  6510  mulassnqg  7571  prarloc  7690  prmuloc  7753  addasssrg  7943  axaddass  8059  ghmgrp  13655