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Theorem axrep5 4543
 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 1818 . . . . 5
2 impexp 447 . . . . . . . 8
32albii 1687 . . . . . . 7
4 19.21v 1778 . . . . . . 7
53, 4bitr2i 253 . . . . . 6
65exbii 1714 . . . . 5
71, 6bitr3i 254 . . . 4
87albii 1687 . . 3
9 nfv 1754 . . . . 5
10 axrep5.1 . . . . 5
119, 10nfan 1986 . . . 4
1211axrep4 4542 . . 3
138, 12sylbi 198 . 2
14 anabs5 816 . . . . . 6
1514exbii 1714 . . . . 5
1615bibi2i 314 . . . 4
1716albii 1687 . . 3
1817exbii 1714 . 2
1913, 18sylib 199 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435  wex 1659  wnf 1663 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-rep 4538 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664 This theorem is referenced by:  zfrepclf  4544  axsep  4547
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