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Theorem 19.33-2 38063
Description: Theorem *11.421 in [WhiteheadRussell] p. 163. Theorem 19.33 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.33-2 ((∀𝑥𝑦𝜑 ∨ ∀𝑥𝑦𝜓) → ∀𝑥𝑦(𝜑𝜓))

Proof of Theorem 19.33-2
StepHypRef Expression
1 orc 400 . . 3 (𝜑 → (𝜑𝜓))
212alimi 1737 . 2 (∀𝑥𝑦𝜑 → ∀𝑥𝑦(𝜑𝜓))
3 olc 399 . . 3 (𝜓 → (𝜑𝜓))
432alimi 1737 . 2 (∀𝑥𝑦𝜓 → ∀𝑥𝑦(𝜑𝜓))
52, 4jaoi 394 1 ((∀𝑥𝑦𝜑 ∨ ∀𝑥𝑦𝜓) → ∀𝑥𝑦(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 383  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
This theorem depends on definitions:  df-bi 197  df-or 385
This theorem is referenced by: (None)
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