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Theorem acneq 7686
 Description: Equality theorem for the choice set function. (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
acneq AC AC

Proof of Theorem acneq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq1 2356 . . . 4
2 oveq2 5882 . . . . 5
3 raleq 2749 . . . . . 6
43exbidv 1616 . . . . 5
52, 4raleqbidv 2761 . . . 4
61, 5anbi12d 691 . . 3
76abbidv 2410 . 2
8 df-acn 7591 . 2 AC
9 df-acn 7591 . 2 AC
107, 8, 93eqtr4g 2353 1 AC AC
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wex 1531   wceq 1632   wcel 1696  cab 2282  wral 2556  cvv 2801   cdif 3162  c0 3468  cpw 3638  csn 3653  cfv 5271  (class class class)co 5874   cmap 6788  AC wacn 7587 This theorem is referenced by:  acndom  7694  dfacacn  7783  dfac13  7784 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ov 5877  df-acn 7591
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