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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 2715 | . . 3 | |
2 | 1 | elima 4934 | . 2 |
3 | df-br 3967 | . . . 4 | |
4 | opelopabsb 4221 | . . . 4 | |
5 | sbsbc 2941 | . . . . . 6 | |
6 | 5 | sbbii 1745 | . . . . 5 |
7 | sbsbc 2941 | . . . . 5 | |
8 | 6, 7 | bitr2i 184 | . . . 4 |
9 | 3, 4, 8 | 3bitri 205 | . . 3 |
10 | 9 | rexbii 2464 | . 2 |
11 | nfs1v 1919 | . . 3 | |
12 | nfv 1508 | . . 3 | |
13 | sbequ12r 1752 | . . 3 | |
14 | 11, 12, 13 | cbvrex 2677 | . 2 |
15 | 2, 10, 14 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wsb 1742 wcel 2128 wrex 2436 wsbc 2937 cop 3563 class class class wbr 3966 copab 4025 cima 4590 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-xp 4593 df-cnv 4595 df-dm 4597 df-rn 4598 df-res 4599 df-ima 4600 |
This theorem is referenced by: (None) |
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