New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > inrab2 | Unicode version |
Description: Intersection with a restricted class abstraction. (Contributed by NM, 19-Nov-2007.) |
Ref | Expression |
---|---|
inrab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2623 | . . 3 | |
2 | abid2 2470 | . . . 4 | |
3 | 2 | eqcomi 2357 | . . 3 |
4 | 1, 3 | ineq12i 3455 | . 2 |
5 | df-rab 2623 | . . 3 | |
6 | inab 3522 | . . . 4 | |
7 | elin 3219 | . . . . . . 7 | |
8 | 7 | anbi1i 676 | . . . . . 6 |
9 | an32 773 | . . . . . 6 | |
10 | 8, 9 | bitri 240 | . . . . 5 |
11 | 10 | abbii 2465 | . . . 4 |
12 | 6, 11 | eqtr4i 2376 | . . 3 |
13 | 5, 12 | eqtr4i 2376 | . 2 |
14 | 4, 13 | eqtr4i 2376 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 358 wceq 1642 wcel 1710 cab 2339 crab 2618 cin 3208 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |