Theorem biantrud

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 2-Aug-1994) (Proof shortened by Wolf Lammen, 23-Oct-2013)

	Ref	Expression
Hypothesis	biantrud.1	⊢ ( 𝜑 → 𝜓 )
Assertion	biantrud	⊢ ( 𝜑 → ( 𝜒 ↔ ( 𝜒 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		biantrud.1	⊢ ( 𝜑 → 𝜓 )
2		iba	⊢ ( 𝜓 → ( 𝜒 ↔ ( 𝜒 ∧ 𝜓 ) ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝜒 ↔ ( 𝜒 ∧ 𝜓 ) ) )