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Theorem axrep2 4347
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfe1 1749 . . . . 5
2 nfv 1630 . . . . 5
31, 2nfim 1834 . . . 4
43nfex 1867 . . 3
5 elequ2 1732 . . . . . . . . 9
65anbi1d 687 . . . . . . . 8
76exbidv 1637 . . . . . . 7
87bibi2d 311 . . . . . 6
98albidv 1636 . . . . 5
109imbi2d 309 . . . 4
1110exbidv 1637 . . 3
12 axrep1 4346 . . 3
134, 11, 12chvar 1971 . 2
14 sp 1765 . . . . . . 7
1514imim1i 57 . . . . . 6
1615alimi 1569 . . . . 5
1716eximi 1586 . . . 4
18 nfv 1630 . . . . 5
19 nfa1 1808 . . . . . . 7
20 nfv 1630 . . . . . . 7
2119, 20nfim 1834 . . . . . 6
2221nfal 1866 . . . . 5
23 equequ2 1700 . . . . . . 7
2423imbi2d 309 . . . . . 6
2524albidv 1636 . . . . 5
2618, 22, 25cbvex 1986 . . . 4
2717, 26sylib 190 . . 3
2827imim1i 57 . 2
2913, 28eximii 1588 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551 This theorem is referenced by:  axrep3  4348  axrepndlem1  8498 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 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-rep 4345 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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