Theorem bj-imim21i

Description: The propositional function ( ph -> ( . -> ps ) ) is decreasing. Its associated inference is syl5 . (Contributed by BJ, 19-Jul-2019)

	Ref	Expression
Hypothesis	bj-imim21i.1	⊢ ( 𝜑 → 𝜓 )
Assertion	bj-imim21i	⊢ ( ( 𝜒 → ( 𝜓 → 𝜃 ) ) → ( 𝜒 → ( 𝜑 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		bj-imim21i.1	⊢ ( 𝜑 → 𝜓 )
2		bj-imim21	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 → ( 𝜓 → 𝜃 ) ) → ( 𝜒 → ( 𝜑 → 𝜃 ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜒 → ( 𝜓 → 𝜃 ) ) → ( 𝜒 → ( 𝜑 → 𝜃 ) ) )