Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opeqex | Unicode version |
Description: Equivalence of existence implied by equality of ordered pairs. (Contributed by NM, 28-May-2008.) |
Ref | Expression |
---|---|
opeqex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2101 | . . 3 | |
2 | 1 | exbidv 1706 | . 2 |
3 | opm 3971 | . 2 | |
4 | opm 3971 | . 2 | |
5 | 2, 3, 4 | 3bitr3g 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 cvv 2557 cop 3378 |
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-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 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: epelg 4027 |
Copyright terms: Public domain | W3C validator |