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Theorem ac2 7971
 Description: Axiom of Choice equivalent. By using restricted quantifiers, we can express the Axiom of Choice with a single explicit conjunction. (If you want to figure it out, the rewritten equivalent ac3 7972 is easier to understand.) Note: aceq0 7629 shows the logical equivalence to ax-ac 7969. (Contributed by NM, 18-Jul-1996.)
Assertion
Ref Expression
ac2
Distinct variable group:   ,,,,,

Proof of Theorem ac2
StepHypRef Expression
1 ax-ac 7969 . 2
2 aceq0 7629 . 2
31, 2mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621  wral 2509  wrex 2510  wreu 2511 This theorem is referenced by:  ac3  7972 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-ac 7969 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-rex 2514  df-reu 2515
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