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Theorem ac7 8054
Description: An Axiom of Choice equivalent similar to the Axiom of Choice (first form) of [Enderton] p. 49. (Contributed by NM, 29-Apr-2004.)
Assertion
Ref Expression
ac7  |-  E. f
( f  C_  x  /\  f  Fn  dom  x )
Distinct variable group:    x, f

Proof of Theorem ac7
StepHypRef Expression
1 df-ac 7697 . 2  |-  (CHOICE  <->  A. x E. f ( f  C_  x  /\  f  Fn  dom  x ) )
21axaci 8049 1  |-  E. f
( f  C_  x  /\  f  Fn  dom  x )
Colors of variables: wff set class
Syntax hints:    /\ wa 360   E.wex 1537    C_ wss 3113   dom cdm 4647    Fn wfn 4654
This theorem is referenced by:  ac7g  8055
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 1927  ax-ext 2237  ax-rep 4091  ax-sep 4101  ax-nul 4109  ax-pow 4146  ax-pr 4172  ax-un 4470  ax-ac2 8043
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-mo 2122  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2521  df-rex 2522  df-reu 2523  df-rab 2525  df-v 2759  df-sbc 2953  df-csb 3043  df-dif 3116  df-un 3118  df-in 3120  df-ss 3127  df-nul 3417  df-if 3526  df-pw 3587  df-sn 3606  df-pr 3607  df-op 3609  df-uni 3788  df-iun 3867  df-br 3984  df-opab 4038  df-mpt 4039  df-id 4267  df-xp 4661  df-rel 4662  df-cnv 4663  df-co 4664  df-dm 4665  df-rn 4666  df-res 4667  df-ima 4668  df-fun 4669  df-fn 4670  df-f 4671  df-f1 4672  df-fo 4673  df-f1o 4674  df-fv 4675  df-ac 7697
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