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Theorem zfrepclf 4554
 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:   ,,   ,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem zfrepclf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 zfrepclf.2 . 2
2 zfrepclf.1 . . . . . 6
32nfeq2 2622 . . . . 5
4 eleq2 2516 . . . . . 6
5 zfrepclf.3 . . . . . 6
64, 5syl6bi 228 . . . . 5
73, 6alrimi 1863 . . . 4
8 nfv 1694 . . . . 5
98axrep5 4553 . . . 4
107, 9syl 16 . . 3
114anbi1d 704 . . . . . . 7
123, 11exbid 1872 . . . . . 6
1312bibi2d 318 . . . . 5
1413albidv 1700 . . . 4
1514exbidv 1701 . . 3
1610, 15mpbid 210 . 2
171, 16vtocle 3169 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1381   wceq 1383  wex 1599   wcel 1804  wnfc 2591  cvv 3095 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-rep 4548 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-v 3097 This theorem is referenced by:  zfrep3cl  4555  zfrep4  4556
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