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Theorem ralun 3445
 Description: Restricted quantification over union. (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
ralun ((x A φ x B φ) → x (AB)φ)

Proof of Theorem ralun
StepHypRef Expression
1 ralunb 3444 . 2 (x (AB)φ ↔ (x A φ x B φ))
21biimpri 197 1 ((x A φ x B φ) → x (AB)φ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∀wral 2614   ∪ cun 3207 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214 This theorem is referenced by: (None)
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