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Theorem cardval3 7831
 Description: An alternative definition of the value of that does not require AC to prove. (Contributed by Mario Carneiro, 7-Jan-2013.) (Revised by Mario Carneiro, 27-Apr-2015.)
Assertion
Ref Expression
cardval3
Distinct variable group:   ,

Proof of Theorem cardval3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2956 . 2
2 isnum2 7824 . . . 4
3 rabn0 3639 . . . 4
4 intex 4348 . . . 4
52, 3, 43bitr2i 265 . . 3
65biimpi 187 . 2
7 breq2 4208 . . . . 5
87rabbidv 2940 . . . 4
98inteqd 4047 . . 3
10 df-card 7818 . . 3
119, 10fvmptg 5796 . 2
121, 6, 11syl2anc 643 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725   wne 2598  wrex 2698  crab 2701  cvv 2948  c0 3620  cint 4042   class class class wbr 4204  con0 4573   cdm 4870  cfv 5446   cen 7098  ccrd 7814 This theorem is referenced by:  cardid2  7832  oncardval  7834  cardidm  7838  cardne  7844  cardval  8413 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-int 4043  df-br 4205  df-opab 4259  df-mpt 4260  df-tr 4295  df-eprel 4486  df-id 4490  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-fv 5454  df-en 7102  df-card 7818
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