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Theorem axrep1 4324
 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 4323 axrep1 4324 axrep2 4325 axrepnd 8474 zfcndrep 8494 = ax-rep 4323. (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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elequ2 1731 . . . . . . . . 9
21anbi1d 687 . . . . . . . 8
32exbidv 1637 . . . . . . 7
43bibi2d 311 . . . . . 6
54albidv 1636 . . . . 5
65exbidv 1637 . . . 4
76imbi2d 309 . . 3
8 ax-rep 4323 . . . 4
9 19.3v 1678 . . . . . . . 8
109imbi1i 317 . . . . . . 7
1110albii 1576 . . . . . 6
1211exbii 1593 . . . . 5
1312albii 1576 . . . 4
14 nfv 1630 . . . . . . 7
15 nfe1 1748 . . . . . . 7
1614, 15nfbi 1857 . . . . . 6
1716nfal 1865 . . . . 5
18 nfv 1630 . . . . 5
19 elequ2 1731 . . . . . . 7
209anbi2i 677 . . . . . . . . 9
2120exbii 1593 . . . . . . . 8
2221a1i 11 . . . . . . 7
2319, 22bibi12d 314 . . . . . 6
2423albidv 1636 . . . . 5
2517, 18, 24cbvex 1984 . . . 4
268, 13, 253imtr3i 258 . . 3
277, 26chvarv 1970 . 2
282719.35ri 1613 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551 This theorem is referenced by:  axrep2  4325 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-rep 4323 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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