Metamath Proof Explorer

Theorem confun2

Description: Confun simplified to two propositions. (Contributed by Jarvin Udandy, 6-Sep-2020)

	Ref	Expression
Hypotheses	confun2.1	$⊢ ψ \to φ$
	confun2.2	$⊢ ψ \to \neg (ψ \to (ψ \land \neg ψ))$
	confun2.3	$⊢ (ψ \to φ) \to ((ψ \to φ) \to φ)$
Assertion	confun2	$⊢ ψ \to (\neg (ψ \to (ψ \land \neg ψ)) \leftrightarrow (ψ \to φ))$

Step	Hyp	Ref	Expression
1		confun2.1	$⊢ ψ \to φ$
2		confun2.2	$⊢ ψ \to \neg (ψ \to (ψ \land \neg ψ))$
3		confun2.3	$⊢ (ψ \to φ) \to ((ψ \to φ) \to φ)$
4	1 1 2 3	confun	$⊢ ψ \to (\neg (ψ \to (ψ \land \neg ψ)) \leftrightarrow (ψ \to φ))$