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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 2733 | . . 3 | |
2 | 1 | elima 4958 | . 2 |
3 | df-br 3990 | . . . 4 | |
4 | opelopabsb 4245 | . . . 4 | |
5 | sbsbc 2959 | . . . . . 6 | |
6 | 5 | sbbii 1758 | . . . . 5 |
7 | sbsbc 2959 | . . . . 5 | |
8 | 6, 7 | bitr2i 184 | . . . 4 |
9 | 3, 4, 8 | 3bitri 205 | . . 3 |
10 | 9 | rexbii 2477 | . 2 |
11 | nfs1v 1932 | . . 3 | |
12 | nfv 1521 | . . 3 | |
13 | sbequ12r 1765 | . . 3 | |
14 | 11, 12, 13 | cbvrex 2693 | . 2 |
15 | 2, 10, 14 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wsb 1755 wcel 2141 wrex 2449 wsbc 2955 cop 3586 class class class wbr 3989 copab 4049 cima 4614 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-xp 4617 df-cnv 4619 df-dm 4621 df-rn 4622 df-res 4623 df-ima 4624 |
This theorem is referenced by: (None) |
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