![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > opeq12i | Unicode version |
Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.) (Proof shortened by Eric Schmidt, 4-Apr-2007.) |
Ref | Expression |
---|---|
opeq1i.1 |
![]() ![]() ![]() ![]() |
opeq12i.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
opeq12i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1i.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | opeq12i.2 |
. 2
![]() ![]() ![]() ![]() | |
3 | opeq12 3715 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | mp2an 423 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 |
This theorem is referenced by: addpinq1 7296 genipv 7341 ltexpri 7445 recexpr 7470 cauappcvgprlemladdru 7488 cauappcvgprlemladdrl 7489 cauappcvgpr 7494 caucvgprlemcl 7508 caucvgprlemladdrl 7510 caucvgpr 7514 caucvgprprlemval 7520 caucvgprprlemnbj 7525 caucvgprprlemmu 7527 caucvgprprlemclphr 7537 caucvgprprlemaddq 7540 caucvgprprlem1 7541 caucvgprprlem2 7542 caucvgsr 7634 pitonnlem1 7677 axi2m1 7707 axcaucvg 7732 |
Copyright terms: Public domain | W3C validator |