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Theorem axrep2 4030
 Description: Axiom of Replacement expressed with the fewest number of different variables and without any restrictions on . (Contributed by NM, 15-Aug-2003.)
Assertion
Ref Expression
axrep2
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem axrep2
StepHypRef Expression
1 nfe1 1566 . . . . 5
2 nfv 1629 . . . . 5
31, 2nfim 1735 . . . 4
43nfex 1733 . . 3
5 elequ2 1832 . . . . . . . . 9
65anbi1d 688 . . . . . . . 8
76exbidv 2005 . . . . . . 7
87bibi2d 311 . . . . . 6
98albidv 2004 . . . . 5
109imbi2d 309 . . . 4
1110exbidv 2005 . . 3
12 axrep1 4029 . . 3
134, 11, 12chvar 1878 . 2
14 ax-4 1692 . . . . . . . 8
1514imim1i 56 . . . . . . 7
1615alimi 1546 . . . . . 6
1716eximi 1574 . . . . 5
18 nfv 1629 . . . . . 6
19 nfa1 1719 . . . . . . . 8
20 nfv 1629 . . . . . . . 8
2119, 20nfim 1735 . . . . . . 7
2221nfal 1732 . . . . . 6
23 equequ2 1830 . . . . . . . 8
2423imbi2d 309 . . . . . . 7
2524albidv 2004 . . . . . 6
2618, 22, 25cbvex 1877 . . . . 5
2717, 26sylib 190 . . . 4
2827imim1i 56 . . 3
2928eximi 1574 . 2
3013, 29ax-mp 10 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621 This theorem is referenced by:  axrep3  4031  axrepndlem1  8094 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-14 1626  ax-17 1628  ax-9 1684  ax-4 1692  ax-ext 2234  ax-rep 4028 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-cleq 2246  df-clel 2249
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