Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2233 | . . . . . . . 8 | |
2 | fvopab3ig.1 | . . . . . . . 8 | |
3 | 1, 2 | anbi12d 470 | . . . . . . 7 |
4 | fvopab3ig.2 | . . . . . . . 8 | |
5 | 4 | anbi2d 461 | . . . . . . 7 |
6 | 3, 5 | opelopabg 4251 | . . . . . 6 |
7 | 6 | biimpar 295 | . . . . 5 |
8 | 7 | exp43 370 | . . . 4 |
9 | 8 | pm2.43a 51 | . . 3 |
10 | 9 | imp 123 | . 2 |
11 | fvopab3ig.4 | . . . 4 | |
12 | 11 | fveq1i 5495 | . . 3 |
13 | funopab 5231 | . . . . 5 | |
14 | fvopab3ig.3 | . . . . . 6 | |
15 | moanimv 2094 | . . . . . 6 | |
16 | 14, 15 | mpbir 145 | . . . . 5 |
17 | 13, 16 | mpgbir 1446 | . . . 4 |
18 | funopfv 5534 | . . . 4 | |
19 | 17, 18 | ax-mp 5 | . . 3 |
20 | 12, 19 | eqtrid 2215 | . 2 |
21 | 10, 20 | syl6 33 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wmo 2020 wcel 2141 cop 3584 copab 4047 wfun 5190 cfv 5196 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-iota 5158 df-fun 5198 df-fv 5204 |
This theorem is referenced by: fvmptg 5570 fvopab6 5590 ov6g 5988 |
Copyright terms: Public domain | W3C validator |