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Theorem rabswap 3464
Description: Swap with a membership relation in a restricted class abstraction. (Contributed by NM, 4-Jul-2005.)
Assertion
Ref Expression
rabswap {𝑥𝐴𝑥𝐵} = {𝑥𝐵𝑥𝐴}

Proof of Theorem rabswap
StepHypRef Expression
1 ancom 464 . 2 ((𝑥𝐴𝑥𝐵) ↔ (𝑥𝐵𝑥𝐴))
21rabbia2 3452 1 {𝑥𝐴𝑥𝐵} = {𝑥𝐵𝑥𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  wcel 2114  {crab 3134
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 1911  ax-6 1970  ax-7 2015  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-rab 3139
This theorem is referenced by:  incom  4152
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