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Mirrors > Home > ILE Home > Th. List > op2nda | Unicode version |
Description: Extract the second member of an ordered pair. (See op1sta 5110 to extract the first member and op2ndb 5112 for an alternate version.) (Contributed by NM, 17-Feb-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
cnvsn.1 |
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cnvsn.2 |
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Ref | Expression |
---|---|
op2nda |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsn.1 |
. . . 4
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2 | 1 | rnsnop 5109 |
. . 3
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3 | 2 | unieqi 3819 |
. 2
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4 | cnvsn.2 |
. . 3
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5 | 4 | unisn 3825 |
. 2
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6 | 3, 5 | eqtri 2198 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-xp 4632 df-rel 4633 df-cnv 4634 df-dm 4636 df-rn 4637 |
This theorem is referenced by: elxp4 5116 elxp5 5117 op2nd 6147 fo2nd 6158 f2ndres 6160 ixpsnf1o 6735 xpassen 6829 xpdom2 6830 |
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