Theorem ad4ant234 1208

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

Hypothesis

Ref	Expression
ad4ant3.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
ad4ant234	|- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )

Proof of Theorem ad4ant234

Step	Hyp	Ref	Expression
1		ad4ant3.1	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expa 1193	. 2 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
3	2	adantlll 472	1 |- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

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 970

This theorem is referenced by: (None)