Theorem expcomdg

Description: Biconditional form of expcomd . (Contributed by Alan Sare, 22-Jul-2012) (New usage is discouraged.)

	Ref	Expression
Assertion	expcomdg	⊢ ( ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ) ↔ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		ancomst	⊢ ( ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ↔ ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) )
2		impexp	⊢ ( ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) ↔ ( 𝜒 → ( 𝜓 → 𝜃 ) ) )
3	1 2	bitri	⊢ ( ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ↔ ( 𝜒 → ( 𝜓 → 𝜃 ) ) )
4	3	imbi2i	⊢ ( ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) ) ↔ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) ) )