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Theorem axrep1 4029
 Description: The version of the Axiom of Replacement used in the Metamath Solitaire applet http://us.metamath.org/mmsolitaire/mms.html. Equivalence is shown via the path ax-rep 4028 axrep1 4029 axrep2 4030 axrepnd 8096 zfcndrep 8116 = ax-rep 4028. (Contributed by NM, 19-Nov-2005.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
axrep1
Distinct variable groups:   ,   ,,
Allowed substitution hints:   (,)

Proof of Theorem axrep1
StepHypRef Expression
1 eleq2 2314 . . . . . . . . 9
21anbi1d 688 . . . . . . . 8
32exbidv 2005 . . . . . . 7
43bibi2d 311 . . . . . 6
54albidv 2004 . . . . 5
65exbidv 2005 . . . 4
76imbi2d 309 . . 3
8 ax-rep 4028 . . . 4
9 nfv 1629 . . . . . . . . 9
10919.3 1760 . . . . . . . 8
1110imbi1i 317 . . . . . . 7
1211albii 1554 . . . . . 6
1312exbii 1580 . . . . 5
1413albii 1554 . . . 4
15 nfv 1629 . . . . . . 7
16 nfe1 1566 . . . . . . 7
1715, 16nfbi 1738 . . . . . 6
1817nfal 1732 . . . . 5
19 nfv 1629 . . . . 5
20 elequ2 1832 . . . . . . 7
2110anbi2i 678 . . . . . . . . 9
2221exbii 1580 . . . . . . . 8
2322a1i 12 . . . . . . 7
2420, 23bibi12d 314 . . . . . 6
2524albidv 2004 . . . . 5
2618, 19, 25cbvex 1877 . . . 4
278, 14, 263imtr3i 258 . . 3
287, 27chvarv 2059 . 2
292819.35ri 1601 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:  axrep2  4030 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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