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Theorem isarep1 4985
 Description: Part of a study of the Axiom of Replacement used by the Isabelle prover. The object PrimReplace is apparently the image of the function encoded by i.e. the class . If so, we can prove Isabelle's "Axiom of Replacement" conclusion without using the Axiom of Replacement, for which I (N. Megill) currently have no explanation. (Contributed by NM, 26-Oct-2006.) (Proof shortened by Mario Carneiro, 4-Dec-2016.)
Assertion
Ref Expression
isarep1
Distinct variable groups:   ,   ,,
Allowed substitution hints:   (,,)   (,)

Proof of Theorem isarep1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2560 . . 3
21elima 4673 . 2
3 df-br 3765 . . . 4
4 opelopabsb 3997 . . . 4
5 sbsbc 2768 . . . . . 6
65sbbii 1648 . . . . 5
7 sbsbc 2768 . . . . 5
86, 7bitr2i 174 . . . 4
93, 4, 83bitri 195 . . 3
109rexbii 2331 . 2
11 nfs1v 1815 . . 3
12 nfv 1421 . . 3
13 sbequ12r 1655 . . 3
1411, 12, 13cbvrex 2530 . 2
152, 10, 143bitri 195 1
 Colors of variables: wff set class Syntax hints:   wb 98   wcel 1393  wsb 1645  wrex 2307  wsbc 2764  cop 3378   class class class wbr 3764  copab 3817  cima 4348 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-xp 4351  df-cnv 4353  df-dm 4355  df-rn 4356  df-res 4357  df-ima 4358 This theorem is referenced by: (None)
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