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Mirrors > Home > ILE Home > Th. List > 1st2nd | Unicode version |
Description: Reconstruction of a member of a relation in terms of its ordered pair components. (Contributed by NM, 29-Aug-2006.) |
Ref | Expression |
---|---|
1st2nd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rel 4654 |
. . 3
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2 | ssel2 3165 |
. . 3
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3 | 1, 2 | sylanb 284 |
. 2
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4 | 1st2nd2 6204 |
. 2
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5 | 3, 4 | syl 14 |
1
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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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 ax-un 4454 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-uni 3828 df-br 4022 df-opab 4083 df-mpt 4084 df-id 4314 df-xp 4653 df-rel 4654 df-cnv 4655 df-co 4656 df-dm 4657 df-rn 4658 df-iota 5199 df-fun 5240 df-fv 5246 df-1st 6169 df-2nd 6170 |
This theorem is referenced by: 2ndrn 6212 1st2ndbr 6213 elopabi 6224 cnvf1olem 6253 exmidapne 7294 aptap 8642 fsumcnv 11486 fprodcnv 11674 |
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