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Theorem ggen31 38239
Description: gen31 38325 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ggen31.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
ggen31 (𝜑 → (𝜓 → (𝜒 → ∀𝑥𝜃)))
Distinct variable groups:   𝜒,𝑥   𝜑,𝑥   𝜓,𝑥
Allowed substitution hint:   𝜃(𝑥)

Proof of Theorem ggen31
StepHypRef Expression
1 ggen31.1 . . . 4 (𝜑 → (𝜓 → (𝜒𝜃)))
21imp 445 . . 3 ((𝜑𝜓) → (𝜒𝜃))
32alrimdv 1854 . 2 ((𝜑𝜓) → (𝜒 → ∀𝑥𝜃))
43ex 450 1 (𝜑 → (𝜓 → (𝜒 → ∀𝑥𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836
This theorem depends on definitions:  df-bi 197  df-an 386
This theorem is referenced by:  onfrALTlem2  38240  gen31  38325
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