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Metamath Proof Explorer

Theorem ee22an

Description: e22an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee22an.1	$⊢ φ \to (ψ \to χ)$
	ee22an.2	$⊢ φ \to (ψ \to θ)$
	ee22an.3	$⊢ (χ \land θ) \to τ$
Assertion	ee22an	$⊢ φ \to (ψ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		ee22an.1	$⊢ φ \to (ψ \to χ)$
2		ee22an.2	$⊢ φ \to (ψ \to θ)$
3		ee22an.3	$⊢ (χ \land θ) \to τ$
4	3	ex	$⊢ χ \to (θ \to τ)$
5	1 2 4	syl6c	$⊢ φ \to (ψ \to τ)$