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Mirrors > Home > ILE Home > Th. List > op1sta | Unicode version |
Description: Extract the first member of an ordered pair. (See op2nda 5134 to extract the second member and op1stb 4499 for an alternate version.) (Contributed by Raph Levien, 4-Dec-2003.) |
Ref | Expression |
---|---|
cnvsn.1 |
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cnvsn.2 |
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Ref | Expression |
---|---|
op1sta |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsn.2 |
. . . 4
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2 | 1 | dmsnop 5123 |
. . 3
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3 | 2 | unieqi 3837 |
. 2
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4 | cnvsn.1 |
. . 3
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5 | 4 | unisn 3843 |
. 2
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6 | 3, 5 | eqtri 2210 |
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-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 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-dm 4657 |
This theorem is referenced by: op1st 6175 fo1st 6186 f1stres 6188 xpassen 6860 xpdom2 6861 |
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