Theorem bj-mp2d

Description: A double modus ponens inference. Inference associated with mpcom . (Contributed by BJ, 24-Sep-2019)

	Ref	Expression
Hypotheses	bj-mp2d.1	⊢ 𝜑
	bj-mp2d.2	⊢ ( 𝜑 → 𝜓 )
	bj-mp2d.3	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
Assertion	bj-mp2d	⊢ 𝜒

Proof

Step	Hyp	Ref	Expression
1		bj-mp2d.1	⊢ 𝜑
2		bj-mp2d.2	⊢ ( 𝜑 → 𝜓 )
3		bj-mp2d.3	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
4	1 2	ax-mp	⊢ 𝜓
5	4 1 3	mp2	⊢ 𝜒