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Theorem rabbid 3456
Description: Version of rabbidv 3437 with disjoint variable condition replaced by nonfreeness hypothesis. (Contributed by BJ, 27-Apr-2019.)
Hypotheses
Ref Expression
rabbid.n 𝑥𝜑
rabbid.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
rabbid (𝜑 → {𝑥𝐴𝜓} = {𝑥𝐴𝜒})

Proof of Theorem rabbid
StepHypRef Expression
1 rabbid.n . 2 𝑥𝜑
2 rabbid.1 . . 3 (𝜑 → (𝜓𝜒))
32adantr 480 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
41, 3rabbida 3455 1 (𝜑 → {𝑥𝐴𝜓} = {𝑥𝐴𝜒})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1534  wnf 1778  wcel 2099  {crab 3429
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-9 2109  ax-12 2167  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2706  df-cleq 2720  df-rab 3430
This theorem is referenced by:  satfv1  34973  bj-rabeqbid  36399  bj-seex  36400
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