Theorem ad4ant14 518

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 481	. 2 |- ( ( ( ph /\ th ) /\ ps ) -> ch )
3	2	adantlr 481	1 |- ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  ad5ant15  525  ad5ant25  528  seqfeq4g  10982  prodmodclem2  12362  prodmodc  12363  zproddc  12364  fprod2d  12408  gcdsupex  12752  gcdsupcl  12753  grpinvalem  13756  gzsumwsubmcl  13852  gzsumwmhm  13854  subrngintm  14571  plyco  15912  gausslemma2dlem1f1o  16301