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Theorem rabswap 2482
 Description: Swap with a membership relation in a restricted class abstraction. (Contributed by NM, 4-Jul-2005.)
Assertion
Ref Expression
rabswap {x Ax B} = {x Bx A}

Proof of Theorem rabswap
StepHypRef Expression
1 ancom 253 . . 3 ((x A x B) ↔ (x B x A))
21abbii 2150 . 2 {x ∣ (x A x B)} = {x ∣ (x B x A)}
3 df-rab 2309 . 2 {x Ax B} = {x ∣ (x A x B)}
4 df-rab 2309 . 2 {x Bx A} = {x ∣ (x B x A)}
52, 3, 43eqtr4i 2067 1 {x Ax B} = {x Bx A}
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   = wceq 1242   ∈ wcel 1390  {cab 2023  {crab 2304 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-rab 2309 This theorem is referenced by: (None)
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