Theorem ggen31

Description: gen31 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ggen31.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion	ggen31	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ∀ 𝑥 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ggen31.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2	1	imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
3	2	alrimdv	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → ∀ 𝑥 𝜃 ) )
4	3	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ∀ 𝑥 𝜃 ) ) )