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Theorem 19.33 1414
Description: Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
19.33 ((∀𝑥𝜑 ∨ ∀𝑥𝜓) → ∀𝑥(𝜑𝜓))

Proof of Theorem 19.33
StepHypRef Expression
1 orc 666 . . 3 (𝜑 → (𝜑𝜓))
21alimi 1385 . 2 (∀𝑥𝜑 → ∀𝑥(𝜑𝜓))
3 olc 665 . . 3 (𝜓 → (𝜑𝜓))
43alimi 1385 . 2 (∀𝑥𝜓 → ∀𝑥(𝜑𝜓))
52, 4jaoi 669 1 ((∀𝑥𝜑 ∨ ∀𝑥𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 662  wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-gen 1379
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.33b2  1561
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