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Theorem rabidim2 39700
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 3218 . 2 (𝑥 ∈ {𝑥𝐴𝜑} ↔ (𝑥𝐴𝜑))
21simprbi 483 1 (𝑥 ∈ {𝑥𝐴𝜑} → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2103  {crab 3018
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-12 2160  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1599  df-ex 1818  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-rab 3023
This theorem is referenced by:  infnsuprnmpt  39881  pimrecltpos  41342  pimiooltgt  41344  pimrecltneg  41356  smfaddlem1  41394  smflimlem2  41403  smfrec  41419  smfmullem4  41424  smfdiv  41427  smfsupxr  41445  smfinflem  41446  smflimsuplem7  41455  smflimsuplem8  41456
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