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Theorem zfrep4 4576
 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:   ,,   ,   ,,
Allowed substitution hints:   ()   (,)

Proof of Theorem zfrep4
StepHypRef Expression
1 abid 2444 . . . . 5
21anbi1i 695 . . . 4
32exbii 1668 . . 3
43abbii 2591 . 2
5 nfab1 2621 . . . . 5
6 zfrep4.1 . . . . 5
7 zfrep4.2 . . . . . 6
81, 7sylbi 195 . . . . 5
95, 6, 8zfrepclf 4574 . . . 4
10 abeq2 2581 . . . . 5
1110exbii 1668 . . . 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  wal 1393   wceq 1395  wex 1613   wcel 1819  cab 2442  cvv 3109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-rep 4568 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111 This theorem is referenced by:  zfpair  4693  cshwsexa  12803
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