Theorem biantru

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	biantru.1	⊢ 𝜑
Assertion	biantru	⊢ ( 𝜓 ↔ ( 𝜓 ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		biantru.1	⊢ 𝜑
2		iba	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜓 ∧ 𝜑 ) ) )
3	1 2	ax-mp	⊢ ( 𝜓 ↔ ( 𝜓 ∧ 𝜑 ) )