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Theorem fv3 5892
 Description: Alternate definition of the value of a function. Definition 6.11 of [TakeutiZaring] p. 26. (Contributed by NM, 30-Apr-2004.) (Revised by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
fv3
Distinct variable groups:   ,,   ,,

Proof of Theorem fv3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elfv 5877 . . 3
2 biimpr 203 . . . . . . . . . 10
32alimi 1692 . . . . . . . . 9
4 vex 3034 . . . . . . . . . 10
5 breq2 4399 . . . . . . . . . 10
64, 5ceqsalv 3061 . . . . . . . . 9
73, 6sylib 201 . . . . . . . 8
87anim2i 579 . . . . . . 7
98eximi 1715 . . . . . 6
10 elequ2 1918 . . . . . . . 8
11 breq2 4399 . . . . . . . 8
1210, 11anbi12d 725 . . . . . . 7
1312cbvexv 2130 . . . . . 6
149, 13sylib 201 . . . . 5
15 exsimpr 1738 . . . . . 6
16 df-eu 2323 . . . . . 6
1715, 16sylibr 217 . . . . 5
1814, 17jca 541 . . . 4
19 nfeu1 2329 . . . . . . 7
20 nfv 1769 . . . . . . . . 9
21 nfa1 1999 . . . . . . . . 9
2220, 21nfan 2031 . . . . . . . 8
2322nfex 2050 . . . . . . 7
2419, 23nfim 2023 . . . . . 6
25 biimp 198 . . . . . . . . . . . . . 14
26 ax9 1917 . . . . . . . . . . . . . 14
2725, 26syl6 33 . . . . . . . . . . . . 13
2827com23 80 . . . . . . . . . . . 12
2928impd 438 . . . . . . . . . . 11
3029sps 1963 . . . . . . . . . 10
3130anc2ri 567 . . . . . . . . 9
3231com12 31 . . . . . . . 8
3332eximdv 1772 . . . . . . 7
3416, 33syl5bi 225 . . . . . 6
3524, 34exlimi 2015 . . . . 5
3635imp 436 . . . 4
3718, 36impbii 192 . . 3
381, 37bitri 257 . 2
3938abbi2i 2586 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  wex 1671   wcel 1904  weu 2319  cab 2457   class class class wbr 4395  cfv 5589 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-iota 5553  df-fv 5597 This theorem is referenced by: (None)
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