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Mirrors > Home > ILE Home > Th. List > isarep1 | Unicode version |
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.) |
Ref | Expression |
---|---|
isarep1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2560 | . . 3 | |
2 | 1 | elima 4673 | . 2 |
3 | df-br 3765 | . . . 4 | |
4 | opelopabsb 3997 | . . . 4 | |
5 | sbsbc 2768 | . . . . . 6 | |
6 | 5 | sbbii 1648 | . . . . 5 |
7 | sbsbc 2768 | . . . . 5 | |
8 | 6, 7 | bitr2i 174 | . . . 4 |
9 | 3, 4, 8 | 3bitri 195 | . . 3 |
10 | 9 | rexbii 2331 | . 2 |
11 | nfs1v 1815 | . . 3 | |
12 | nfv 1421 | . . 3 | |
13 | sbequ12r 1655 | . . 3 | |
14 | 11, 12, 13 | cbvrex 2530 | . 2 |
15 | 2, 10, 14 | 3bitri 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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