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Theorem rabidim2 40037
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 3298 . 2 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
21simprbi 491 1 (𝑥 ∈ {𝑥𝐴𝜑} → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2157  {crab 3094
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-12 2213  ax-ext 2778
This theorem depends on definitions:  df-bi 199  df-an 386  df-tru 1657  df-ex 1876  df-sb 2065  df-clab 2787  df-cleq 2793  df-clel 2796  df-rab 3099
This theorem is referenced by:  infnsuprnmpt  40207  pimrecltpos  41660  pimiooltgt  41662  pimrecltneg  41674  smfaddlem1  41712  smflimlem2  41721  smfrec  41737  smfmullem4  41742  smfdiv  41745  smfsupxr  41763  smfinflem  41764  smflimsuplem7  41773  smflimsuplem8  41774
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