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Theorem axrep5 4318
 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 1922 . . . . 5
2 impexp 434 . . . . . . . 8
32albii 1575 . . . . . . 7
4 19.21v 1913 . . . . . . 7
53, 4bitr2i 242 . . . . . 6
65exbii 1592 . . . . 5
71, 6bitr3i 243 . . . 4
87albii 1575 . . 3
9 nfv 1629 . . . . 5
10 axrep5.1 . . . . 5
119, 10nfan 1846 . . . 4
1211axrep4 4317 . . 3
138, 12sylbi 188 . 2
14 anabs5 785 . . . . . 6
1514exbii 1592 . . . . 5
1615bibi2i 305 . . . 4
1716albii 1575 . . 3
1817exbii 1592 . 2
1913, 18sylib 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  zfrepclf  4319  axsep  4322 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-rep 4313 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554
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