Theorem ad4ant14 514

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Hypothesis

Ref	Expression
ad4ant2.1	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
ad4ant14	|- ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) -> ch )

Proof of Theorem ad4ant14

Step	Hyp	Ref	Expression
1		ad4ant2.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2	1	adantlr 477	. 2 |- ( ( ( ph /\ th ) /\ ps ) -> ch )
3	2	adantlr 477	1 |- ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104

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 is referenced by:  ad5ant15  521  ad5ant25  524  seqfeq4g  10678  prodmodclem2  11921  prodmodc  11922  zproddc  11923  fprod2d  11967  gcdsupex  12311  gcdsupcl  12312  grpinvalem  13250  gsumwsubmcl  13361  gsumwmhm  13363  subrngintm  14007  plyco  15264  gausslemma2dlem1f1o  15570