Theorem bianir

Description: A closed form of mpbir , analogous to pm2.27 (assertion). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Roger Witte, 17-Aug-2020)

	Ref	Expression
Assertion	bianir	⊢ ( ( 𝜑 ∧ ( 𝜓 ↔ 𝜑 ) ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		biimpr	⊢ ( ( 𝜓 ↔ 𝜑 ) → ( 𝜑 → 𝜓 ) )
2	1	impcom	⊢ ( ( 𝜑 ∧ ( 𝜓 ↔ 𝜑 ) ) → 𝜓 )