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Mirrors > Home > MPE Home > Th. List > isarep1 | Structured version Visualization version 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 3203 | . . 3 | |
2 | 1 | elima 5471 | . 2 |
3 | df-br 4654 | . . . 4 | |
4 | opelopabsb 4985 | . . . 4 | |
5 | sbsbc 3439 | . . . . . 6 | |
6 | 5 | sbbii 1887 | . . . . 5 |
7 | sbsbc 3439 | . . . . 5 | |
8 | 6, 7 | bitr2i 265 | . . . 4 |
9 | 3, 4, 8 | 3bitri 286 | . . 3 |
10 | 9 | rexbii 3041 | . 2 |
11 | nfs1v 2437 | . . 3 | |
12 | nfv 1843 | . . 3 | |
13 | sbequ12r 2112 | . . 3 | |
14 | 11, 12, 13 | cbvrex 3168 | . 2 |
15 | 2, 10, 14 | 3bitri 286 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wsb 1880 wcel 1990 wrex 2913 wsbc 3435 cop 4183 class class class wbr 4653 copab 4712 cima 5117 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: (None) |
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