Theorem bj-imim21 32539

Description: The propositional function ( ch -> ( period -> th ) ) is decreasing. (Contributed by BJ, 19-Jul-2019.)

Assertion

Ref	Expression
bj-imim21	|- ( ( ph -> ps ) -> ( ( ch -> ( ps -> th ) ) -> ( ch -> ( ph -> th ) ) ) )

Proof of Theorem bj-imim21

Step	Hyp	Ref	Expression
1		imim1 83	. 2 |- ( ( ph -> ps ) -> ( ( ps -> th ) -> ( ph -> th ) ) )
2	1	imim2d 57	1 |- ( ( ph -> ps ) -> ( ( ch -> ( ps -> th ) ) -> ( ch -> ( 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:  bj-imim21i  32540  bj-axc4  32581