Theorem 3imp21 1200

Description: The importation inference 3imp 1195 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) (Revised to shorten 3com12 1209 by Wolf Lammen, 23-Jun-2022.)

Hypothesis

Ref	Expression
3imp31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )

Assertion

Ref	Expression
3imp21	|- ( ( ps /\ ph /\ ch ) -> th )

Proof of Theorem 3imp21

Step	Hyp	Ref	Expression
1		3imp31.1	. . 3 |- ( ph -> ( ps -> ( ch -> th ) ) )
2	1	com13 80	. 2 |- ( ch -> ( ps -> ( ph -> th ) ) )
3	2	3imp231 1199	1 |- ( ( ps /\ ph /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

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

This theorem is referenced by:  lmodvsmmulgdi  13955  gausslemma2dlem1a  15383