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Mirrors > Home > MPE Home > Th. List > opelxp1 | Structured version Visualization version Unicode version |
Description: The first member of an ordered pair of classes in a Cartesian product belongs to first Cartesian product argument. (Contributed by NM, 28-May-2008.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
opelxp1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxp 4883 |
. 2
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2 | 1 | simplbi 466 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4476 df-xp 4859 |
This theorem is referenced by: otelxp1 4888 dff3 6058 ressnop0 6095 swoord1 7418 swoord2 7419 canthp1lem2 9104 ciclcl 15756 txcmplem1 20705 txlm 20712 dvbsss 22906 vcoprnelem 26246 nvvcop 26262 nvvop 26277 prsdm 28769 linedegen 30959 opelopab3 32088 |
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