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Theorem rabidim2 43873
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 3452 . 2 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
21simprbi 497 1 (𝑥 ∈ {𝑥𝐴𝜑} → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2106  {crab 3432
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-12 2171  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433
This theorem is referenced by:  infnsuprnmpt  44033  preimagelt  45494  preimalegt  45495  pimrecltpos  45503  pimiooltgt  45505  pimrecltneg  45519  smfaddlem1  45558  smflimlem2  45567  smfrec  45584  smfmullem4  45589  smfdiv  45592  smfsupxr  45611  smfinflem  45612  smflimsuplem7  45621  smflimsuplem8  45622  fsupdm  45637  finfdm  45641
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