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Mirrors > Home > MPE Home > Th. List > axrep5 | Structured version Visualization version Unicode version |
Description: Axiom of Replacement (similar to Axiom Rep of [BellMachover] p. 463). The antecedent tells us is analogous to a "function" from to (although it is not really a function since it is a wff and not a class). In the consequent we postulate the existence of a set that corresponds to the "image" of restricted to some other set . The hypothesis says must not be free in . (Contributed by NM, 26-Nov-1995.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
axrep5.1 |
Ref | Expression |
---|---|
axrep5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.37v 1910 | . . . . 5 | |
2 | impexp 462 | . . . . . . . 8 | |
3 | 2 | albii 1747 | . . . . . . 7 |
4 | 19.21v 1868 | . . . . . . 7 | |
5 | 3, 4 | bitr2i 265 | . . . . . 6 |
6 | 5 | exbii 1774 | . . . . 5 |
7 | 1, 6 | bitr3i 266 | . . . 4 |
8 | 7 | albii 1747 | . . 3 |
9 | nfv 1843 | . . . . 5 | |
10 | axrep5.1 | . . . . 5 | |
11 | 9, 10 | nfan 1828 | . . . 4 |
12 | 11 | axrep4 4775 | . . 3 |
13 | 8, 12 | sylbi 207 | . 2 |
14 | anabs5 851 | . . . . . 6 | |
15 | 14 | exbii 1774 | . . . . 5 |
16 | 15 | bibi2i 327 | . . . 4 |
17 | 16 | albii 1747 | . . 3 |
18 | 17 | exbii 1774 | . 2 |
19 | 13, 18 | sylib 208 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wex 1704 wnf 1708 |
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-rep 4771 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: zfrepclf 4777 axsep 4780 |
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