Theorem ggen22 45373

Description: gen22 45372 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ggen22.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
ggen22	⊢ (𝜑 → (𝜓 → ∀𝑥∀𝑦𝜒))

Distinct variable groups:   𝜑,𝑥   𝜑,𝑦   𝜓,𝑥   𝜓,𝑦

Allowed substitution hints:   𝜒(𝑥, 𝑦)

Proof of Theorem ggen22

Step	Hyp	Ref	Expression
1		ggen22.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	alrimdv 1962	. 2 ⊢ (𝜑 → (𝜓 → ∀𝑦𝜒))
3	2	alrimdv 1962	1 ⊢ (𝜑 → (𝜓 → ∀𝑥∀𝑦𝜒))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1828  ax-4 1842  ax-5 1943

This theorem is used by: (None)