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Mirrors > Home > ILE Home > Th. List > fvopab3ig | Unicode version |
Description: Value of a function given by ordered-pair class abstraction. (Contributed by NM, 23-Oct-1999.) |
Ref | Expression |
---|---|
fvopab3ig.1 | |
fvopab3ig.2 | |
fvopab3ig.3 | |
fvopab3ig.4 |
Ref | Expression |
---|---|
fvopab3ig |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2200 | . . . . . . . 8 | |
2 | fvopab3ig.1 | . . . . . . . 8 | |
3 | 1, 2 | anbi12d 464 | . . . . . . 7 |
4 | fvopab3ig.2 | . . . . . . . 8 | |
5 | 4 | anbi2d 459 | . . . . . . 7 |
6 | 3, 5 | opelopabg 4185 | . . . . . 6 |
7 | 6 | biimpar 295 | . . . . 5 |
8 | 7 | exp43 369 | . . . 4 |
9 | 8 | pm2.43a 51 | . . 3 |
10 | 9 | imp 123 | . 2 |
11 | fvopab3ig.4 | . . . 4 | |
12 | 11 | fveq1i 5415 | . . 3 |
13 | funopab 5153 | . . . . 5 | |
14 | fvopab3ig.3 | . . . . . 6 | |
15 | moanimv 2072 | . . . . . 6 | |
16 | 14, 15 | mpbir 145 | . . . . 5 |
17 | 13, 16 | mpgbir 1429 | . . . 4 |
18 | funopfv 5454 | . . . 4 | |
19 | 17, 18 | ax-mp 5 | . . 3 |
20 | 12, 19 | syl5eq 2182 | . 2 |
21 | 10, 20 | syl6 33 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wmo 1998 cop 3525 copab 3983 wfun 5112 cfv 5118 |
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 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 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 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-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 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 |
This theorem is referenced by: fvmptg 5490 fvopab6 5510 ov6g 5901 |
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