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Mirrors > Home > ILE Home > Th. List > ovidig | Unicode version |
Description: The value of an operation class abstraction. Compare ovidi 5882. 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 5770 | . 2 | |
2 | ovidig.1 | . . . . 5 | |
3 | 2 | funoprab 5864 | . . . 4 |
4 | ovidig.2 | . . . . 5 | |
5 | 4 | funeqi 5139 | . . . 4 |
6 | 3, 5 | mpbir 145 | . . 3 |
7 | oprabid 5796 | . . . . 5 | |
8 | 7 | biimpri 132 | . . . 4 |
9 | 8, 4 | eleqtrrdi 2231 | . . 3 |
10 | funopfv 5454 | . . 3 | |
11 | 6, 9, 10 | mpsyl 65 | . 2 |
12 | 1, 11 | syl5eq 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wmo 1998 cop 3525 wfun 5112 cfv 5118 (class class class)co 5767 coprab 5768 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-setind 4447 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-iota 5083 df-fun 5120 df-fv 5126 df-ov 5770 df-oprab 5771 |
This theorem is referenced by: ovidi 5882 |
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