Theorem bj-mp2c

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

	Ref	Expression
Hypotheses	bj-mp2c.1	⊢ 𝜑
	bj-mp2c.2	⊢ ( 𝜑 → 𝜓 )
	bj-mp2c.3	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	bj-mp2c	⊢ 𝜒

Proof

Step	Hyp	Ref	Expression
1		bj-mp2c.1	⊢ 𝜑
2		bj-mp2c.2	⊢ ( 𝜑 → 𝜓 )
3		bj-mp2c.3	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	1 2	ax-mp	⊢ 𝜓
5	1 4 3	mp2	⊢ 𝜒