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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 2689 | . . 3 | |
2 | 1 | elima 4886 | . 2 |
3 | df-br 3930 | . . . 4 | |
4 | opelopabsb 4182 | . . . 4 | |
5 | sbsbc 2913 | . . . . . 6 | |
6 | 5 | sbbii 1738 | . . . . 5 |
7 | sbsbc 2913 | . . . . 5 | |
8 | 6, 7 | bitr2i 184 | . . . 4 |
9 | 3, 4, 8 | 3bitri 205 | . . 3 |
10 | 9 | rexbii 2442 | . 2 |
11 | nfs1v 1912 | . . 3 | |
12 | nfv 1508 | . . 3 | |
13 | sbequ12r 1745 | . . 3 | |
14 | 11, 12, 13 | cbvrex 2651 | . 2 |
15 | 2, 10, 14 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1480 wsb 1735 wrex 2417 wsbc 2909 cop 3530 class class class wbr 3929 copab 3988 cima 4542 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-xp 4545 df-cnv 4547 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 |
This theorem is referenced by: (None) |
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