Theorem ad5ant125 1243

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)

Hypothesis

Ref	Expression
ad5ant.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
ad5ant125	|- ( ( ( ( ( ph /\ ps ) /\ ta ) /\ et ) /\ ch ) -> th )

Proof of Theorem ad5ant125

Step	Hyp	Ref	Expression
1		ad5ant.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expia 1207	. . 3 |- ( ( ph /\ ps ) -> ( ch -> th ) )
3	2	2a1d 23	. 2 |- ( ( ph /\ ps ) -> ( ta -> ( et -> ( ch -> th ) ) ) )
4	3	imp41 353	1 |- ( ( ( ( ( ph /\ ps ) /\ ta ) /\ et ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

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 depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by: (None)