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Mirrors > Home > MPE Home > Th. List > op1sta | Unicode version |
Description: Extract the first member of an ordered pair. (See op2nda 5498 to extract the second member, op1stb 4722 for an alternate version, and op1st 6808 for the preferred version.) (Contributed by Raph Levien, 4-Dec-2003.) |
Ref | Expression |
---|---|
cnvsn.1 | |
cnvsn.2 |
Ref | Expression |
---|---|
op1sta |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsn.2 | . . . 4 | |
2 | 1 | dmsnop 5487 | . . 3 |
3 | 2 | unieqi 4258 | . 2 |
4 | cnvsn.1 | . . 3 | |
5 | 4 | unisn 4264 | . 2 |
6 | 3, 5 | eqtri 2486 | 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1395 e. wcel 1818
cvv 3109
{ csn 4029 <. cop 4035 U. cuni 4249
dom cdm 5004 |
This theorem is referenced by: elxp4 6744 op1st 6808 fo1st 6820 f1stres 6822 xpassen 7631 xpdom2 7632 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-sep 4573 ax-nul 4581 ax-pr 4691 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 975 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-ne 2654 df-rex 2813 df-rab 2816 df-v 3111 df-dif 3478 df-un 3480 df-in 3482 df-ss 3489 df-nul 3785 df-if 3942 df-sn 4030 df-pr 4032 df-op 4036 df-uni 4250 df-br 4453 df-dm 5014 |
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