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Metamath Proof Explorer

Theorem e00an

Description: Elimination rule identical to mp2an . The non-virtual deduction form is the virtual deduction form, which is mp2an . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e00an.1	$⊢ φ$
	e00an.2	$⊢ ψ$
	e00an.3	$⊢ (φ \land ψ) \to χ$
Assertion	e00an	$⊢ χ$

Proof

Step	Hyp	Ref	Expression
1		e00an.1	$⊢ φ$
2		e00an.2	$⊢ ψ$
3		e00an.3	$⊢ (φ \land ψ) \to χ$
4	1 2 3	mp2an	$⊢ χ$