Theorem 3adant1r 1213

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 1186	. . 3 |- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	adantlr 469	. 2 |- ( ( ( ph /\ ta ) /\ ( ps /\ ch ) ) -> th )
4	3	3impb 1181	1 |- ( ( ( ph /\ ta ) /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 963

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 965

This theorem is referenced by:  3adant2r  1215  3adant3r  1217  tfr1onlembacc  6286  tfr1onlembfn  6288  tfr1onlemaccex  6292  tfr1onlemres  6293  tfrcllembfn  6301  tfrcllemaccex  6305  tfrcllemres  6306  tfrcldm  6307  tfrcl  6308  mulassnqg  7299  prarloc  7418  prmuloc  7481  addasssrg  7671  axaddass  7787