Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > op2nda | Unicode version |
Description: Extract the second member of an ordered pair. (See op1sta 4822 to extract the first member and op2ndb 4824 for an alternate version.) (Contributed by NM, 17-Feb-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
cnvsn.1 | |
cnvsn.2 |
Ref | Expression |
---|---|
op2nda |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsn.1 | . . . 4 | |
2 | 1 | rnsnop 4821 | . . 3 |
3 | 2 | unieqi 3611 | . 2 |
4 | cnvsn.2 | . . 3 | |
5 | 4 | unisn 3617 | . 2 |
6 | 3, 5 | eqtri 2101 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wcel 1433 cvv 2601 csn 3398 cop 3401 cuni 3601 crn 4364 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-xp 4369 df-rel 4370 df-cnv 4371 df-dm 4373 df-rn 4374 |
This theorem is referenced by: elxp4 4828 elxp5 4829 op2nd 5794 fo2nd 5805 f2ndres 5807 xpassen 6327 xpdom2 6328 |
Copyright terms: Public domain | W3C validator |