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Theorem axrep2 4510
 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 1935 . . . . 5
2 nfv 1769 . . . . 5
31, 2nfim 2023 . . . 4
43nfex 2050 . . 3
5 elequ2 1918 . . . . . . . . 9
65anbi1d 719 . . . . . . . 8
76exbidv 1776 . . . . . . 7
87bibi2d 325 . . . . . 6
98albidv 1775 . . . . 5
109imbi2d 323 . . . 4
1110exbidv 1776 . . 3
12 axrep1 4509 . . 3
134, 11, 12chvar 2119 . 2
14 sp 1957 . . . . . . 7
1514imim1i 59 . . . . . 6
1615alimi 1692 . . . . 5
1716eximi 1715 . . . 4
18 nfv 1769 . . . . 5
19 nfa1 1999 . . . . . . 7
20 nfv 1769 . . . . . . 7
2119, 20nfim 2023 . . . . . 6
2221nfal 2049 . . . . 5
23 equequ2 1876 . . . . . . 7
2423imbi2d 323 . . . . . 6
2524albidv 1775 . . . . 5
2618, 22, 25cbvex 2128 . . . 4
2717, 26sylib 201 . . 3
2827imim1i 59 . 2
2913, 28eximii 1717 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450  wex 1671 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-rep 4508 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676 This theorem is referenced by:  axrep3  4511  axrepndlem1  9035
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