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Theorem rabidim2 41236
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 3383 . 2 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
21simprbi 497 1 (𝑥 ∈ {𝑥𝐴𝜑} → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  {crab 3146
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-12 2169  ax-ext 2797
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1533  df-ex 1774  df-sb 2063  df-clab 2804  df-cleq 2818  df-clel 2897  df-rab 3151
This theorem is referenced by:  infnsuprnmpt  41389  preimagelt  42848  preimalegt  42849  pimrecltpos  42855  pimiooltgt  42857  pimrecltneg  42869  smfaddlem1  42907  smflimlem2  42916  smfrec  42932  smfmullem4  42937  smfdiv  42940  smfsupxr  42958  smfinflem  42959  smflimsuplem7  42968  smflimsuplem8  42969
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