Theorem biantrur

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 3-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		biantrur.1	⊢ 𝜑
2	1	biantru	⊢ ( 𝜓 ↔ ( 𝜓 ∧ 𝜑 ) )
3	2	biancomi	⊢ ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) )