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Theorem axrep3 4354
 Description: Axiom of Replacement slightly strengthened from axrep2 4353; may occur free in . (Contributed by NM, 2-Jan-1997.)
Assertion
Ref Expression
axrep3
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)

Proof of Theorem axrep3
StepHypRef Expression
1 nfe1 1750 . . . 4
2 nfv 1631 . . . . . 6
3 nfv 1631 . . . . . . . 8
4 nfa1 1809 . . . . . . . 8
53, 4nfan 1849 . . . . . . 7
65nfex 1868 . . . . . 6
72, 6nfbi 1859 . . . . 5
87nfal 1867 . . . 4
91, 8nfim 1835 . . 3
109nfex 1868 . 2
11 elequ2 1733 . . . . . . . 8
1211anbi1d 687 . . . . . . 7
1312exbidv 1638 . . . . . 6
1413bibi2d 311 . . . . 5
1514albidv 1637 . . . 4
1615imbi2d 309 . . 3
1716exbidv 1638 . 2
18 axrep2 4353 . 2
1910, 17, 18chvar 1972 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551 This theorem is referenced by:  axrep4  4355 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 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-rep 4351 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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