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Theorem rabswap 3440
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 460 . 2 ((𝑥𝐴𝑥𝐵) ↔ (𝑥𝐵𝑥𝐴))
21rabbia2 3434 1 {𝑥𝐴𝑥𝐵} = {𝑥𝐵𝑥𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wcel 2105  {crab 3431
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-9 2115  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-rab 3432
This theorem is referenced by:  incom  4201
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