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Mirrors > Home > NFE Home > Th. List > iotaex | Unicode version |
Description: Theorem 8.23 in [Quine] p. 58. This theorem proves the existence of the class under our definition. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotaex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotaval 4351 | . . . . 5 | |
2 | 1 | eqcomd 2358 | . . . 4 |
3 | 2 | eximi 1576 | . . 3 |
4 | df-eu 2208 | . . 3 | |
5 | isset 2864 | . . 3 | |
6 | 3, 4, 5 | 3imtr4i 257 | . 2 |
7 | iotanul 4355 | . . 3 | |
8 | 0ex 4111 | . . 3 | |
9 | 7, 8 | syl6eqel 2441 | . 2 |
10 | 6, 9 | pm2.61i 156 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 176 wal 1540 wex 1541 wceq 1642 wcel 1710 weu 2204 cvv 2860 c0 3551 cio 4338 |
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 ax-nin 4079 |
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 2479 df-ne 2519 df-ral 2620 df-rex 2621 df-v 2862 df-sbc 3048 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 df-sn 3742 df-pr 3743 df-uni 3893 df-iota 4340 |
This theorem is referenced by: iota4an 4359 ncfinex 4473 tfinex 4486 fvex 5340 tcex 6158 |
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