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

Theorem axrep3 4566
 Description: Axiom of Replacement slightly strengthened from axrep2 4565; may occur free in . (Contributed by NM, 2-Jan-1997.)
Assertion
Ref Expression
axrep3
Distinct variable group:   ,,,

Proof of Theorem axrep3
StepHypRef Expression
1 nfe1 1840 . . . 4
2 nfv 1707 . . . . . 6
3 nfv 1707 . . . . . . . 8
4 nfa1 1897 . . . . . . . 8
53, 4nfan 1928 . . . . . . 7
65nfex 1948 . . . . . 6
72, 6nfbi 1934 . . . . 5
87nfal 1947 . . . 4
91, 8nfim 1920 . . 3
109nfex 1948 . 2
11 elequ2 1823 . . . . . . . 8
1211anbi1d 704 . . . . . . 7
1312exbidv 1714 . . . . . 6
1413bibi2d 318 . . . . 5
1514albidv 1713 . . . 4
1615imbi2d 316 . . 3
1716exbidv 1714 . 2
18 axrep2 4565 . 2
1910, 17, 18chvar 2013 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612 This theorem is referenced by:  axrep4  4567 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-rep 4563 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617
 Copyright terms: Public domain W3C validator