Theorem bj-imbi12

Description: Uncurried (imported) form of imbi12 . (Contributed by BJ, 6-May-2019)

	Ref	Expression
Assertion	bj-imbi12	⊢ ( ( ( 𝜑 ↔ 𝜓 ) ∧ ( 𝜒 ↔ 𝜃 ) ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imbi12	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 ↔ 𝜃 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) ) )
2	1	imp	⊢ ( ( ( 𝜑 ↔ 𝜓 ) ∧ ( 𝜒 ↔ 𝜃 ) ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )