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Theorem 19.33 1800
Description: Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
19.33 ((∀𝑥𝜑 ∨ ∀𝑥𝜓) → ∀𝑥(𝜑𝜓))

Proof of Theorem 19.33
StepHypRef Expression
1 orc 398 . . 3 (𝜑 → (𝜑𝜓))
21alimi 1729 . 2 (∀𝑥𝜑 → ∀𝑥(𝜑𝜓))
3 olc 397 . . 3 (𝜓 → (𝜑𝜓))
43alimi 1729 . 2 (∀𝑥𝜓 → ∀𝑥(𝜑𝜓))
52, 4jaoi 392 1 ((∀𝑥𝜑 ∨ ∀𝑥𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727
This theorem depends on definitions:  df-bi 195  df-or 383
This theorem is referenced by:  19.33b  1801
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