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	$$⊢\phi$$
	bj-mp2d.2	$$⊢\phi \to \psi$$
	bj-mp2d.3	$$⊢\psi \to \left(\phi \to \chi \right)$$
Assertion	bj-mp2d	$$⊢\chi$$

Proof

Step	Hyp	Ref	Expression
1		bj-mp2d.1	$$⊢\phi$$
2		bj-mp2d.2	$$⊢\phi \to \psi$$
3		bj-mp2d.3	$$⊢\psi \to \left(\phi \to \chi \right)$$
4	1 2	ax-mp	$$⊢\psi$$
5	4 1 3	mp2	$$⊢\chi$$