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Theorem bj-rabbid 33221
Description: Version of rabbidv 3329 with dv condition replaced by non-freeness hypothesis. (Contributed by BJ, 27-Apr-2019.)
Hypotheses
Ref Expression
bj-rabbid.nf 𝑥𝜑
bj-rabbid.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
bj-rabbid (𝜑 → {𝑥𝐴𝜓} = {𝑥𝐴𝜒})

Proof of Theorem bj-rabbid
StepHypRef Expression
1 bj-rabbid.nf . 2 𝑥𝜑
2 bj-rabbid.1 . . 3 (𝜑 → (𝜓𝜒))
32adantr 472 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
41, 3bj-rabbida 33220 1 (𝜑 → {𝑥𝐴𝜓} = {𝑥𝐴𝜒})
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1632  wnf 1857  wcel 2139  {crab 3054
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-ral 3055  df-rab 3059
This theorem is referenced by:  bj-rabeqbid  33223  bj-seex  33225
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