Theorem biimt

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

	Ref	Expression
Assertion	biimt	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( 𝜓 → ( 𝜑 → 𝜓 ) )
2		pm2.27	⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
3	1 2	impbid2	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 → 𝜓 ) ) )