Theorem mpbidi

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994)

	Ref	Expression
Hypotheses	mpbidi.min	$$⊢\theta \to \left(\phi \to \psi \right)$$
	mpbidi.maj	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	mpbidi	$$⊢\theta \to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		mpbidi.min	$$⊢\theta \to \left(\phi \to \psi \right)$$
2		mpbidi.maj	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
3	2	biimpd	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	1 3	sylcom	$$⊢\theta \to \left(\phi \to \chi \right)$$