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Metamath Proof Explorer

Theorem ee02an

Description: e02an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee02an.1	$⊢ φ$
	ee02an.2	$⊢ ψ \to (χ \to θ)$
	ee02an.3	$⊢ (φ \land θ) \to τ$
Assertion	ee02an	$⊢ ψ \to (χ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		ee02an.1	$⊢ φ$
2		ee02an.2	$⊢ ψ \to (χ \to θ)$
3		ee02an.3	$⊢ (φ \land θ) \to τ$
4	3	ex	$⊢ φ \to (θ \to τ)$
5	1 2 4	mpsylsyld	$⊢ ψ \to (χ \to τ)$