Theorem ad5ant14 512

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

Hypothesis

Ref	Expression
ad5ant2.1	|- ( ( ph /\ ps ) -> ch )

Assertion

Ref	Expression
ad5ant14	|- ( ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) /\ et ) -> ch )

Proof of Theorem ad5ant14

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 |- ( ( ph /\ ps ) -> ch )
2	1	adantlr 469	. 2 |- ( ( ( ph /\ th ) /\ ps ) -> ch )
3	2	ad4ant13 505	1 |- ( ( ( ( ( ph /\ th ) /\ ta ) /\ ps ) /\ et ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103

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 is referenced by: (None)