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Theorem zfrepclf 4569
 Description: An inference rule based on the Axiom of Replacement. Typically, defines a function from to . (Contributed by NM, 26-Nov-1995.)
Hypotheses
Ref Expression
zfrepclf.1
zfrepclf.2
zfrepclf.3
Assertion
Ref Expression
zfrepclf
Distinct variable groups:   ,,   ,   ,,

Proof of Theorem zfrepclf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 zfrepclf.2 . 2
2 zfrepclf.1 . . . . . 6
32nfeq2 2636 . . . . 5
4 eleq2 2530 . . . . . 6
5 zfrepclf.3 . . . . . 6
64, 5syl6bi 228 . . . . 5
73, 6alrimi 1877 . . . 4
8 nfv 1707 . . . . 5
98axrep5 4568 . . . 4
107, 9syl 16 . . 3
114anbi1d 704 . . . . . . 7
123, 11exbid 1886 . . . . . 6
1312bibi2d 318 . . . . 5
1413albidv 1713 . . . 4
1514exbidv 1714 . . 3
1610, 15mpbid 210 . 2
171, 16vtocle 3183 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  F/_wnfc 2605   cvv 3109 This theorem is referenced by:  zfrep3cl  4570  zfrep4  4571 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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-rep 4563 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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