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Theorem zfrep4 4571
Description: A version of Replacement using class abstractions. (Contributed by NM, 26-Nov-1995.)
Hypotheses
Ref Expression
zfrep4.1
zfrep4.2
Assertion
Ref Expression
zfrep4
Distinct variable groups:   , ,   ,   , ,

Proof of Theorem zfrep4
StepHypRef Expression
1 abid 2444 . . . . 5
21anbi1i 695 . . . 4
32exbii 1667 . . 3
43abbii 2591 . 2
5 nfab1 2621 . . . . 5
6 zfrep4.1 . . . . 5
7 zfrep4.2 . . . . . 6
81, 7sylbi 195 . . . . 5
95, 6, 8zfrepclf 4569 . . . 4
10 abeq2 2581 . . . . 5
1110exbii 1667 . . . 4
129, 11mpbir 209 . . 3
1312issetri 3116 . 2
144, 13eqeltrri 2542 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  {cab 2442   cvv 3109
This theorem is referenced by:  zfpair  4689  cshwsexa  12792
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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