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Metamath Proof Explorer

Theorem ee11an

Description: e11an without virtual deductions. syl22anc is also e11an without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee11an.1	$⊢ φ \to ψ$
	ee11an.2	$⊢ φ \to χ$
	ee11an.3	$⊢ (ψ \land χ) \to θ$
Assertion	ee11an	$⊢ φ \to θ$

Proof

Step	Hyp	Ref	Expression
1		ee11an.1	$⊢ φ \to ψ$
2		ee11an.2	$⊢ φ \to χ$
3		ee11an.3	$⊢ (ψ \land χ) \to θ$
4	3	ex	$⊢ ψ \to (χ \to θ)$
5	1 2 4	sylc	$⊢ φ \to θ$