Theorem imbi2d

Description: Deduction adding an antecedent to both sides of a logical equivalence. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypothesis	imbid.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	imbi2d	⊢ ( 𝜑 → ( ( 𝜃 → 𝜓 ) ↔ ( 𝜃 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imbid.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2	1	a1d	⊢ ( 𝜑 → ( 𝜃 → ( 𝜓 ↔ 𝜒 ) ) )
3	2	pm5.74d	⊢ ( 𝜑 → ( ( 𝜃 → 𝜓 ) ↔ ( 𝜃 → 𝜒 ) ) )