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Theorem tz6.12f 5490
 Description: Function value, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 30-Aug-1999.)
Hypothesis
Ref Expression
tz6.12f.1
Assertion
Ref Expression
tz6.12f
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem tz6.12f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opeq2 3738 . . . . 5
21eleq1d 2223 . . . 4
3 tz6.12f.1 . . . . . . 7
43nfel2 2309 . . . . . 6
5 nfv 1505 . . . . . 6
64, 5, 2cbveu 2027 . . . . 5
76a1i 9 . . . 4
82, 7anbi12d 465 . . 3
9 eqeq2 2164 . . 3
108, 9imbi12d 233 . 2
11 tz6.12 5489 . 2
1210, 11chvarv 1914 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332  weu 2003   wcel 2125  wnfc 2283  cop 3559  cfv 5163 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-eu 2006  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-rex 2438  df-v 2711  df-sbc 2934  df-un 3102  df-sn 3562  df-pr 3563  df-op 3565  df-uni 3769  df-br 3962  df-iota 5128  df-fv 5171 This theorem is referenced by: (None)
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