Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  axrep3 Structured version   Unicode version

Theorem axrep3 4477
 Description: Axiom of Replacement slightly strengthened from axrep2 4476; 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 1894 . . . 4
2 nfv 1755 . . . . . 6
3 nfv 1755 . . . . . . . 8
4 nfa1 1956 . . . . . . . 8
53, 4nfan 1988 . . . . . . 7
65nfex 2008 . . . . . 6
72, 6nfbi 1994 . . . . 5
87nfal 2007 . . . 4
91, 8nfim 1980 . . 3
109nfex 2008 . 2
11 elequ2 1877 . . . . . . . 8
1211anbi1d 709 . . . . . . 7
1312exbidv 1762 . . . . . 6
1413bibi2d 319 . . . . 5
1514albidv 1761 . . . 4
1615imbi2d 317 . . 3
1716exbidv 1762 . 2
18 axrep2 4476 . 2
1910, 17, 18chvar 2073 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435  wex 1657 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-rep 4474 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662 This theorem is referenced by:  axrep4  4478
 Copyright terms: Public domain W3C validator