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Theorem axrep5 4138
 Description: Axiom of Replacement (similar to Axiom Rep of [BellMachover] p. 463). The antecedent tells us is analogous to a "function" from to (although it is not really a function since it is a wff and not a class). In the consequent we postulate the existence of a set that corresponds to the "image" of restricted to some other set . The hypothesis says must not be free in . (Contributed by NM, 26-Nov-1995.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypothesis
Ref Expression
axrep5.1
Assertion
Ref Expression
axrep5
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)

Proof of Theorem axrep5
StepHypRef Expression
1 19.37v 1842 . . . . 5
2 impexp 433 . . . . . . . 8
32albii 1555 . . . . . . 7
4 19.21v 1833 . . . . . . 7
53, 4bitr2i 241 . . . . . 6
65exbii 1571 . . . . 5
71, 6bitr3i 242 . . . 4
87albii 1555 . . 3
9 nfv 1607 . . . . 5
10 axrep5.1 . . . . 5
119, 10nfan 1773 . . . 4
1211axrep4 4137 . . 3
138, 12sylbi 187 . 2
14 anabs5 784 . . . . . 6
1514exbii 1571 . . . . 5
1615bibi2i 304 . . . 4
1716albii 1555 . . 3
1817exbii 1571 . 2
1913, 18sylib 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1529  wex 1530  wnf 1533   wceq 1625   wcel 1686 This theorem is referenced by:  zfrepclf  4139  axsep  4142 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-14 1690  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266  ax-rep 4133 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-cleq 2278  df-clel 2281
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