This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem biimt

Description: A wff is equivalent to itself with true antecedent. (Contributed by NM, 28-Jan-1996)

		Ref	Expression
	Assertion	biimt	$⊢ φ \to (ψ \leftrightarrow (φ \to ψ))$

Step	Hyp	Ref	Expression
1		ax-1	$⊢ ψ \to (φ \to ψ)$
2		pm2.27	$⊢ φ \to ((φ \to ψ) \to ψ)$
3	1 2	impbid2	$⊢ φ \to (ψ \leftrightarrow (φ \to ψ))$