Metamath Proof Explorer

Theorem impexpd

Description: The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. After the User's Proof was completed, it was minimized. The completed User's Proof before minimization is not shown. (Contributed by Alan Sare, 18-Mar-2012) (Proof modification is discouraged.) (New usage is discouraged.)

1::	\|- ( ( ( ps /\ ch ) -> th ) <-> ( ps -> ( ch -> th ) ) )
qed:1:	\|- ( ( ph -> ( ( ps /\ ch ) -> th ) ) <-> ( ph -> ( ps -> ( ch -> th ) ) ) )

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

Proof

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