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Mirrors > Home > NFE Home > Th. List > difrab | Unicode version |
Description: Difference of two restricted class abstractions. (Contributed by NM, 23-Oct-2004.) |
Ref | Expression |
---|---|
difrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2623 | . . 3 | |
2 | df-rab 2623 | . . 3 | |
3 | 1, 2 | difeq12i 3383 | . 2 |
4 | df-rab 2623 | . . 3 | |
5 | difab 3523 | . . . 4 | |
6 | anass 630 | . . . . . 6 | |
7 | simpr 447 | . . . . . . . . 9 | |
8 | 7 | con3i 127 | . . . . . . . 8 |
9 | 8 | anim2i 552 | . . . . . . 7 |
10 | pm3.2 434 | . . . . . . . . . 10 | |
11 | 10 | adantr 451 | . . . . . . . . 9 |
12 | 11 | con3d 125 | . . . . . . . 8 |
13 | 12 | imdistani 671 | . . . . . . 7 |
14 | 9, 13 | impbii 180 | . . . . . 6 |
15 | 6, 14 | bitr3i 242 | . . . . 5 |
16 | 15 | abbii 2465 | . . . 4 |
17 | 5, 16 | eqtr4i 2376 | . . 3 |
18 | 4, 17 | eqtr4i 2376 | . 2 |
19 | 3, 18 | eqtr4i 2376 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 358 wceq 1642 wcel 1710 cab 2339 crab 2618 cdif 3206 |
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 2478 df-rab 2623 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 |
This theorem is referenced by: (None) |
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