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Mirrors > Home > MPE Home > Th. List > axrep2 | Structured version Visualization version Unicode version |
Description: Axiom of Replacement expressed with the fewest number of different variables and without any restrictions on . (Contributed by NM, 15-Aug-2003.) |
Ref | Expression |
---|---|
axrep2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2027 | . . . . 5 | |
2 | nfv 1843 | . . . . 5 | |
3 | 1, 2 | nfim 1825 | . . . 4 |
4 | 3 | nfex 2154 | . . 3 |
5 | elequ2 2004 | . . . . . . . . 9 | |
6 | 5 | anbi1d 741 | . . . . . . . 8 |
7 | 6 | exbidv 1850 | . . . . . . 7 |
8 | 7 | bibi2d 332 | . . . . . 6 |
9 | 8 | albidv 1849 | . . . . 5 |
10 | 9 | imbi2d 330 | . . . 4 |
11 | 10 | exbidv 1850 | . . 3 |
12 | axrep1 4772 | . . 3 | |
13 | 4, 11, 12 | chvar 2262 | . 2 |
14 | sp 2053 | . . . . . . 7 | |
15 | 14 | imim1i 63 | . . . . . 6 |
16 | 15 | alimi 1739 | . . . . 5 |
17 | 16 | eximi 1762 | . . . 4 |
18 | nfv 1843 | . . . . 5 | |
19 | nfa1 2028 | . . . . . . 7 | |
20 | nfv 1843 | . . . . . . 7 | |
21 | 19, 20 | nfim 1825 | . . . . . 6 |
22 | 21 | nfal 2153 | . . . . 5 |
23 | equequ2 1953 | . . . . . . 7 | |
24 | 23 | imbi2d 330 | . . . . . 6 |
25 | 24 | albidv 1849 | . . . . 5 |
26 | 18, 22, 25 | cbvex 2272 | . . . 4 |
27 | 17, 26 | sylib 208 | . . 3 |
28 | 27 | imim1i 63 | . 2 |
29 | 13, 28 | eximii 1764 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wex 1704 |
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: axrep3 4774 axrepndlem1 9414 |
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