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Mirrors > Home > ILE Home > Th. List > oprabrexex2 | Unicode version |
Description: Existence of an existentially restricted operation abstraction. (Contributed by Jeff Madsen, 11-Jun-2010.) |
Ref | Expression |
---|---|
oprabrexex2.1 | |
oprabrexex2.2 |
Ref | Expression |
---|---|
oprabrexex2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-oprab 5830 | . . 3 | |
2 | rexcom4 2735 | . . . . 5 | |
3 | rexcom4 2735 | . . . . . . 7 | |
4 | rexcom4 2735 | . . . . . . . . 9 | |
5 | r19.42v 2614 | . . . . . . . . . 10 | |
6 | 5 | exbii 1585 | . . . . . . . . 9 |
7 | 4, 6 | bitri 183 | . . . . . . . 8 |
8 | 7 | exbii 1585 | . . . . . . 7 |
9 | 3, 8 | bitri 183 | . . . . . 6 |
10 | 9 | exbii 1585 | . . . . 5 |
11 | 2, 10 | bitr2i 184 | . . . 4 |
12 | 11 | abbii 2273 | . . 3 |
13 | 1, 12 | eqtri 2178 | . 2 |
14 | oprabrexex2.1 | . . 3 | |
15 | df-oprab 5830 | . . . 4 | |
16 | oprabrexex2.2 | . . . 4 | |
17 | 15, 16 | eqeltrri 2231 | . . 3 |
18 | 14, 17 | abrexex2 6074 | . 2 |
19 | 13, 18 | eqeltri 2230 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1335 wex 1472 wcel 2128 cab 2143 wrex 2436 cvv 2712 cop 3564 coprab 5827 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-coll 4081 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-iun 3853 df-br 3968 df-opab 4028 df-mpt 4029 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-f 5176 df-f1 5177 df-fo 5178 df-f1o 5179 df-fv 5180 df-oprab 5830 |
This theorem is referenced by: (None) |
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