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Theorem axrep1 4148
 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 4147 axrep1 4148 axrep2 4149 axrepnd 8232 zfcndrep 8252 = ax-rep 4147. (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 eleq2 2357 . . . . . . . . 9
21anbi1d 685 . . . . . . . 8
32exbidv 1616 . . . . . . 7
43bibi2d 309 . . . . . 6
54albidv 1615 . . . . 5
65exbidv 1616 . . . 4
76imbi2d 307 . . 3
8 ax-rep 4147 . . . 4
9 nfv 1609 . . . . . . . . 9
10919.3 1793 . . . . . . . 8
1110imbi1i 315 . . . . . . 7
1211albii 1556 . . . . . 6
1312exbii 1572 . . . . 5
1413albii 1556 . . . 4
15 nfv 1609 . . . . . . 7
16 nfe1 1718 . . . . . . 7
1715, 16nfbi 1784 . . . . . 6
1817nfal 1778 . . . . 5
19 nfv 1609 . . . . 5
20 elequ2 1701 . . . . . . 7
2110anbi2i 675 . . . . . . . . 9
2221exbii 1572 . . . . . . . 8
2322a1i 10 . . . . . . 7
2420, 23bibi12d 312 . . . . . 6
2524albidv 1615 . . . . 5
2618, 19, 25cbvex 1938 . . . 4
278, 14, 263imtr3i 256 . . 3
287, 27chvarv 1966 . 2
292819.35ri 1592 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530  wex 1531   wceq 1632   wcel 1696 This theorem is referenced by:  axrep2  4149 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-rep 4147 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-cleq 2289  df-clel 2292
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