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Metamath Proof Explorer

Theorem e0bi

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

	Ref	Expression
Hypotheses	e0bi.1	$⊢ φ$
	e0bi.2	$⊢ φ \leftrightarrow ψ$
Assertion	e0bi	$⊢ ψ$

Proof

Step	Hyp	Ref	Expression
1		e0bi.1	$⊢ φ$
2		e0bi.2	$⊢ φ \leftrightarrow ψ$
3	1 2	mpbi	$⊢ ψ$