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Theorem rabidim2 44094
Description: Membership in a restricted abstraction, implication. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Assertion
Ref Expression
rabidim2 (𝑥 ∈ {𝑥𝐴𝜑} → 𝜑)

Proof of Theorem rabidim2
StepHypRef Expression
1 rabid 3451 . 2 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
21simprbi 496 1 (𝑥 ∈ {𝑥𝐴𝜑} → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  {crab 3431
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-12 2170  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-rab 3432
This theorem is referenced by:  infnsuprnmpt  44254  preimagelt  45715  preimalegt  45716  pimrecltpos  45724  pimiooltgt  45726  pimrecltneg  45740  smfaddlem1  45779  smflimlem2  45788  smfrec  45805  smfmullem4  45810  smfdiv  45813  smfsupxr  45832  smfinflem  45833  smflimsuplem7  45842  smflimsuplem8  45843  fsupdm  45858  finfdm  45862
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