Metamath Proof Explorer


Theorem bj-imim21

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

Ref Expression
Assertion bj-imim21 ( ( 𝜑𝜓 ) → ( ( 𝜒 → ( 𝜓𝜃 ) ) → ( 𝜒 → ( 𝜑𝜃 ) ) ) )

Proof

Step Hyp Ref Expression
1 imim1 ( ( 𝜑𝜓 ) → ( ( 𝜓𝜃 ) → ( 𝜑𝜃 ) ) )
2 1 imim2d ( ( 𝜑𝜓 ) → ( ( 𝜒 → ( 𝜓𝜃 ) ) → ( 𝜒 → ( 𝜑𝜃 ) ) ) )