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Theorem cdafn 8049
 Description: Cardinal number addition is a function. (Contributed by Mario Carneiro, 28-Apr-2015.)
Assertion
Ref Expression
cdafn

Proof of Theorem cdafn
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-cda 8048 . 2
2 vex 2959 . . . 4
3 snex 4405 . . . 4
42, 3xpex 4990 . . 3
5 vex 2959 . . . 4
6 snex 4405 . . . 4
75, 6xpex 4990 . . 3
84, 7unex 4707 . 2
91, 8fnmpt2i 6420 1
 Colors of variables: wff set class Syntax hints:  cvv 2956   cun 3318  c0 3628  csn 3814   cxp 4876   wfn 5449  c1o 6717   ccda 8047 This theorem is referenced by:  cda1dif  8056  cdacomen  8061  cdadom1  8066  cdainf  8072  pwcdadom  8096 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-fv 5462  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350  df-cda 8048
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