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Mirrors > Home > ILE Home > Th. List > abrexco | Unicode version |
Description: Composition of two image maps and . (Contributed by NM, 27-May-2013.) |
Ref | Expression |
---|---|
abrexco.1 | |
abrexco.2 |
Ref | Expression |
---|---|
abrexco |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . . . . 5 | |
2 | vex 2560 | . . . . . . . . 9 | |
3 | eqeq1 2046 | . . . . . . . . . 10 | |
4 | 3 | rexbidv 2327 | . . . . . . . . 9 |
5 | 2, 4 | elab 2687 | . . . . . . . 8 |
6 | 5 | anbi1i 431 | . . . . . . 7 |
7 | r19.41v 2466 | . . . . . . 7 | |
8 | 6, 7 | bitr4i 176 | . . . . . 6 |
9 | 8 | exbii 1496 | . . . . 5 |
10 | 1, 9 | bitri 173 | . . . 4 |
11 | rexcom4 2577 | . . . 4 | |
12 | 10, 11 | bitr4i 176 | . . 3 |
13 | abrexco.1 | . . . . 5 | |
14 | abrexco.2 | . . . . . 6 | |
15 | 14 | eqeq2d 2051 | . . . . 5 |
16 | 13, 15 | ceqsexv 2593 | . . . 4 |
17 | 16 | rexbii 2331 | . . 3 |
18 | 12, 17 | bitri 173 | . 2 |
19 | 18 | abbii 2153 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wex 1381 wcel 1393 cab 2026 wrex 2307 cvv 2557 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 |
This theorem is referenced by: (None) |
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