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Theorem tz6.12-2 5399
 Description: Function value when is not a function. Theorem 6.12(2) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
tz6.12-2
Distinct variable groups:   ,   ,

Proof of Theorem tz6.12-2
StepHypRef Expression
1 simpr 449 . . . . 5
21eximi 1574 . . . 4
3 elfv 5375 . . . 4
4 df-eu 2118 . . . 4
52, 3, 43imtr4i 259 . . 3
65con3i 129 . 2
76eq0rdv 3396 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621  weu 2114  c0 3362   class class class wbr 3920  cfv 4592 This theorem is referenced by:  tz6.12i  5401  ndmfv  5405  nfunsn  5410 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-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 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 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-sbc 2922  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-xp 4594  df-cnv 4596  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fv 4608
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