Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE 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 2451 | . . 3 | |
2 | abid2 2285 | . . . 4 | |
3 | 2 | eqcomi 2168 | . . 3 |
4 | 1, 3 | ineq12i 3316 | . 2 |
5 | df-rab 2451 | . . 3 | |
6 | inab 3385 | . . . 4 | |
7 | elin 3300 | . . . . . . 7 | |
8 | 7 | anbi1i 454 | . . . . . 6 |
9 | an32 552 | . . . . . 6 | |
10 | 8, 9 | bitri 183 | . . . . 5 |
11 | 10 | abbii 2280 | . . . 4 |
12 | 6, 11 | eqtr4i 2188 | . . 3 |
13 | 5, 12 | eqtr4i 2188 | . 2 |
14 | 4, 13 | eqtr4i 2188 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1342 wcel 2135 cab 2150 crab 2446 cin 3110 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rab 2451 df-v 2723 df-in 3117 |
This theorem is referenced by: iooval2 9842 fzval2 9938 dfphi2 12131 znnen 12274 |
Copyright terms: Public domain | W3C validator |