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Theorem tz6.12f 5890
 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 4220 . . . . 5
21eleq1d 2536 . . . 4
3 tz6.12f.1 . . . . . . 7
43nfel2 2647 . . . . . 6
5 nfv 1683 . . . . . 6
64, 5, 2cbveu 2318 . . . . 5
76a1i 11 . . . 4
82, 7anbi12d 710 . . 3
9 eqeq2 2482 . . 3
108, 9imbi12d 320 . 2
11 tz6.12 5889 . 2
1210, 11chvarv 1983 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379   wcel 1767  weu 2275  wnfc 2615  cop 4039  cfv 5594 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-iota 5557  df-fv 5602 This theorem is referenced by: (None)
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