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Theorem axrep1 4488
 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 4487 axrep1 4488 axrep2 4489 axrepnd 8845 zfcndrep 8868 = ax-rep 4487. (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 1762 . . . . . . . . 9
21anbi1d 704 . . . . . . . 8
32exbidv 1681 . . . . . . 7
43bibi2d 318 . . . . . 6
54albidv 1680 . . . . 5
65exbidv 1681 . . . 4
76imbi2d 316 . . 3
8 ax-rep 4487 . . . 4
9 19.3v 1719 . . . . . . . 8
109imbi1i 325 . . . . . . 7
1110albii 1611 . . . . . 6
1211exbii 1635 . . . . 5
1312albii 1611 . . . 4
14 nfv 1674 . . . . . . 7
15 nfe1 1779 . . . . . . 7
1614, 15nfbi 1868 . . . . . 6
1716nfal 1874 . . . . 5
18 nfv 1674 . . . . 5
19 elequ2 1762 . . . . . . 7
209anbi2i 694 . . . . . . . . 9
2120exbii 1635 . . . . . . . 8
2221a1i 11 . . . . . . 7
2319, 22bibi12d 321 . . . . . 6
2423albidv 1680 . . . . 5
2517, 18, 24cbvex 1971 . . . 4
268, 13, 253imtr3i 265 . . 3
277, 26chvarv 1959 . 2
282719.35ri 1658 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1368  wex 1587 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-9 1761  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-rep 4487 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591 This theorem is referenced by:  axrep2  4489
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