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Theorem isarep1 5532
 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 2959 . . 3
21elima 5208 . 2
3 df-br 4213 . . . 4
4 opelopabsb 4465 . . . 4
5 sbsbc 3165 . . . . . 6
65sbbii 1665 . . . . 5
7 sbsbc 3165 . . . . 5
86, 7bitr2i 242 . . . 4
93, 4, 83bitri 263 . . 3
109rexbii 2730 . 2
11 nfs1v 2182 . . 3
12 nfv 1629 . . 3
13 sbequ12r 1945 . . 3
1411, 12, 13cbvrex 2929 . 2
152, 10, 143bitri 263 1
 Colors of variables: wff set class Syntax hints:   wb 177  wsb 1658   wcel 1725  wrex 2706  wsbc 3161  cop 3817   class class class wbr 4212  copab 4265  cima 4881 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-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891
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