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Mirrors > Home > NFE Home > Th. List > iotanul | Unicode version |
Description: Theorem 8.22 in [Quine] p. 57. This theorem is the result if there isn't exactly one that satisfies . (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotanul |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eu 2208 | . 2 | |
2 | dfiota2 4340 | . . 3 | |
3 | alnex 1543 | . . . . . 6 | |
4 | ax-1 6 | . . . . . . . . . . 11 | |
5 | eqidd 2354 | . . . . . . . . . . 11 | |
6 | 4, 5 | impbid1 194 | . . . . . . . . . 10 |
7 | 6 | con2bid 319 | . . . . . . . . 9 |
8 | 7 | alimi 1559 | . . . . . . . 8 |
9 | abbi 2463 | . . . . . . . 8 | |
10 | 8, 9 | sylib 188 | . . . . . . 7 |
11 | dfnul2 3552 | . . . . . . 7 | |
12 | 10, 11 | syl6eqr 2403 | . . . . . 6 |
13 | 3, 12 | sylbir 204 | . . . . 5 |
14 | 13 | unieqd 3902 | . . . 4 |
15 | uni0 3918 | . . . 4 | |
16 | 14, 15 | syl6eq 2401 | . . 3 |
17 | 2, 16 | syl5eq 2397 | . 2 |
18 | 1, 17 | sylnbi 297 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wal 1540 wex 1541 wceq 1642 weu 2204 cab 2339 c0 3550 cuni 3891 cio 4337 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-uni 3892 df-iota 4339 |
This theorem is referenced by: iotassuni 4355 iotaex 4356 dfiota3 4370 dfiota4 4372 fvprc 5325 |
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