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Theorem r19.32vr 2503
 Description: One direction of Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers. For decidable propositions this is an equivalence, as seen at r19.32vdc 2504. (Contributed by Jim Kingdon, 19-Aug-2018.)
Assertion
Ref Expression
r19.32vr ((𝜑 ∨ ∀𝑥𝐴 𝜓) → ∀𝑥𝐴 (𝜑𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem r19.32vr
StepHypRef Expression
1 nfv 1462 . 2 𝑥𝜑
21r19.32r 2502 1 ((𝜑 ∨ ∀𝑥𝐴 𝜓) → ∀𝑥𝐴 (𝜑𝜓))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∨ wo 662  ∀wral 2349 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  ax-4 1441  ax-17 1460 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-ral 2354 This theorem is referenced by:  iinuniss  3766
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