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Theorem dfac7 7968
 Description: Equivalence of the Axiom of Choice (first form) of [Enderton] p. 49 and our Axiom of Choice (in the form of ac2 8297). The proof does not depend AC on but does depend on the Axiom of Regularity. (Contributed by Mario Carneiro, 17-May-2015.)
Assertion
Ref Expression
dfac7 CHOICE
Distinct variable group:   ,,,,,

Proof of Theorem dfac7
StepHypRef Expression
1 dfac2 7967 . 2 CHOICE
2 aceq2 7956 . . 3
32albii 1572 . 2
41, 3bitr4i 244 1 CHOICE
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1546  wex 1547   wne 2567  wral 2666  wrex 2667  wreu 2668  c0 3588  CHOICEwac 7952 This theorem is referenced by:  dfac0  7969  dfac1  7970 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pow 4337  ax-pr 4363  ax-un 4660  ax-reg 7516 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-ral 2671  df-rex 2672  df-reu 2673  df-rab 2675  df-v 2918  df-sbc 3122  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-pw 3761  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-mpt 4228  df-eprel 4454  df-id 4458  df-fr 4501  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-rn 4848  df-res 4849  df-ima 4850  df-iota 5377  df-fun 5415  df-fn 5416  df-f 5417  df-fv 5421  df-riota 6508  df-ac 7953
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