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Metamath Proof Explorer

Theorem ee20an

Description: e20an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee20an.1	$⊢ φ \to (ψ \to χ)$
	ee20an.2	$⊢ θ$
	ee20an.3	$⊢ (χ \land θ) \to τ$
Assertion	ee20an	$⊢ φ \to (ψ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		ee20an.1	$⊢ φ \to (ψ \to χ)$
2		ee20an.2	$⊢ θ$
3		ee20an.3	$⊢ (χ \land θ) \to τ$
4	3	ex	$⊢ χ \to (θ \to τ)$
5	1 2 4	syl6mpi	$⊢ φ \to (ψ \to τ)$