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Theorem tz6.12f 5889
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:   ,

Proof of Theorem tz6.12f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opeq2 4218 . . . . 5
21eleq1d 2526 . . . 4
3 tz6.12f.1 . . . . . . 7
43nfel2 2637 . . . . . 6
5 nfv 1707 . . . . . 6
64, 5, 2cbveu 2321 . . . . 5
76a1i 11 . . . 4
82, 7anbi12d 710 . . 3
9 eqeq2 2472 . . 3
108, 9imbi12d 320 . 2
11 tz6.12 5888 . 2
1210, 11chvarv 2014 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282  F/_wnfc 2605  <.cop 4035  `cfv 5593
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601
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