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Mirrors > Home > NFE Home > Th. List > ralidm | Unicode version |
Description: Idempotent law for restricted quantifier. (Contributed by NM, 28-Mar-1997.) |
Ref | Expression |
---|---|
ralidm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rzal 3652 | . . 3 | |
2 | rzal 3652 | . . 3 | |
3 | 1, 2 | 2thd 231 | . 2 |
4 | neq0 3561 | . . 3 | |
5 | biimt 325 | . . . 4 | |
6 | df-ral 2620 | . . . . 5 | |
7 | nfra1 2665 | . . . . . 6 | |
8 | 7 | 19.23 1801 | . . . . 5 |
9 | 6, 8 | bitri 240 | . . . 4 |
10 | 5, 9 | syl6rbbr 255 | . . 3 |
11 | 4, 10 | sylbi 187 | . 2 |
12 | 3, 11 | pm2.61i 156 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wal 1540 wex 1541 wceq 1642 wcel 1710 wral 2615 c0 3551 |
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-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ne 2519 df-ral 2620 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-dif 3216 df-nul 3552 |
This theorem is referenced by: (None) |
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