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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 2399 | . . . . 5 | |
2 | vex 2663 | . . . . . . . . 9 | |
3 | eqeq1 2124 | . . . . . . . . . 10 | |
4 | 3 | rexbidv 2415 | . . . . . . . . 9 |
5 | 2, 4 | elab 2802 | . . . . . . . 8 |
6 | 5 | anbi1i 453 | . . . . . . 7 |
7 | r19.41v 2564 | . . . . . . 7 | |
8 | 6, 7 | bitr4i 186 | . . . . . 6 |
9 | 8 | exbii 1569 | . . . . 5 |
10 | 1, 9 | bitri 183 | . . . 4 |
11 | rexcom4 2683 | . . . 4 | |
12 | 10, 11 | bitr4i 186 | . . 3 |
13 | abrexco.1 | . . . . 5 | |
14 | abrexco.2 | . . . . . 6 | |
15 | 14 | eqeq2d 2129 | . . . . 5 |
16 | 13, 15 | ceqsexv 2699 | . . . 4 |
17 | 16 | rexbii 2419 | . . 3 |
18 | 12, 17 | bitri 183 | . 2 |
19 | 18 | abbii 2233 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wex 1453 wcel 1465 cab 2103 wrex 2394 cvv 2660 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 |
This theorem is referenced by: restco 12270 |
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