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Theorem ggen22 38316
Description: gen22 38315 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ggen22.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
ggen22 (𝜑 → (𝜓 → ∀𝑥𝑦𝜒))
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦   𝜓,𝑥   𝜓,𝑦
Allowed substitution hints:   𝜒(𝑥,𝑦)

Proof of Theorem ggen22
StepHypRef Expression
1 ggen22.1 . . 3 (𝜑 → (𝜓𝜒))
21alrimdv 1859 . 2 (𝜑 → (𝜓 → ∀𝑦𝜒))
32alrimdv 1859 1 (𝜑 → (𝜓 → ∀𝑥𝑦𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1719  ax-4 1734  ax-5 1841
This theorem is referenced by: (None)
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