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Metamath Proof Explorer

Theorem dfvd1ir

Description: Inference form of df-vd1 with the virtual deduction as the assertion. (Contributed by Alan Sare, 14-Nov-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	dfvd1ir.1	$⊢ φ \to ψ$
	Assertion	dfvd1ir	$⊢ (φ \to ψ)$

Proof

Step	Hyp	Ref	Expression
1		dfvd1ir.1	$⊢ φ \to ψ$
2		df-vd1	$⊢ (φ \to ψ) \leftrightarrow (φ \to ψ)$
3	1 2	mpbir	$⊢ (φ \to ψ)$