Theorem syldc 46

Description: Syllogism deduction. Commuted form of syld 45. (Contributed by BJ, 25-Oct-2021.)

Hypotheses

Ref	Expression
syld.1	|- ( ph -> ( ps -> ch ) )
syld.2	|- ( ph -> ( ch -> th ) )

Assertion

Ref	Expression
syldc	|- ( ps -> ( ph -> th ) )

Proof of Theorem syldc

Step	Hyp	Ref	Expression
1		syld.1	. . 3 |- ( ph -> ( ps -> ch ) )
2		syld.2	. . 3 |- ( ph -> ( ch -> th ) )
3	1, 2	syld 45	. 2 |- ( ph -> ( ps -> th ) )
4	3	com12 30	1 |- ( ps -> ( ph -> th ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  dfgrp3mlem  12973