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	$$⊢\phi$$
	bj-mp2c.2	$$⊢\phi \to \psi$$
	bj-mp2c.3	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	bj-mp2c	$$⊢\chi$$

Proof

Step	Hyp	Ref	Expression
1		bj-mp2c.1	$$⊢\phi$$
2		bj-mp2c.2	$$⊢\phi \to \psi$$
3		bj-mp2c.3	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	1 2	ax-mp	$$⊢\psi$$
5	1 4 3	mp2	$$⊢\chi$$