Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ovidig | Unicode version |
Description: The value of an operation class abstraction. Compare ovidi 5619. The condition is been removed. (Contributed by Mario Carneiro, 29-Dec-2014.) |
Ref | Expression |
---|---|
ovidig.1 | |
ovidig.2 |
Ref | Expression |
---|---|
ovidig |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5515 | . 2 | |
2 | ovidig.1 | . . . . 5 | |
3 | 2 | funoprab 5601 | . . . 4 |
4 | ovidig.2 | . . . . 5 | |
5 | 4 | funeqi 4922 | . . . 4 |
6 | 3, 5 | mpbir 134 | . . 3 |
7 | oprabid 5537 | . . . . 5 | |
8 | 7 | biimpri 124 | . . . 4 |
9 | 8, 4 | syl6eleqr 2131 | . . 3 |
10 | funopfv 5213 | . . 3 | |
11 | 6, 9, 10 | mpsyl 59 | . 2 |
12 | 1, 11 | syl5eq 2084 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 wmo 1901 cop 3378 wfun 4896 cfv 4902 (class class class)co 5512 coprab 5513 |
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-in1 544 ax-in2 545 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-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-setind 4262 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 df-ov 5515 df-oprab 5516 |
This theorem is referenced by: ovidi 5619 |
Copyright terms: Public domain | W3C validator |