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Theorem rabswap 2790
 Description: Swap with a membership relation in a restricted class abstraction. (Contributed by NM, 4-Jul-2005.)
Assertion
Ref Expression
rabswap {x A x B} = {x B x A}

Proof of Theorem rabswap
StepHypRef Expression
1 ancom 437 . . 3 ((x A x B) ↔ (x B x A))
21abbii 2465 . 2 {x (x A x B)} = {x (x B x A)}
3 df-rab 2623 . 2 {x A x B} = {x (x A x B)}
4 df-rab 2623 . 2 {x B x A} = {x (x B x A)}
52, 3, 43eqtr4i 2383 1 {x A x B} = {x B x A}
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  {cab 2339  {crab 2618 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-rab 2623 This theorem is referenced by: (None)
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