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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > altopth | Structured version Unicode version |
Description: The alternate ordered
pair theorem. If two alternate ordered pairs are
equal, their first elements are equal and their second elements are
equal. Note that ![]() ![]() ![]() |
Ref | Expression |
---|---|
altopth.1 |
![]() ![]() ![]() ![]() |
altopth.2 |
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Ref | Expression |
---|---|
altopth |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | altopth.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | altopth.2 |
. 2
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3 | altopthg 28165 |
. 2
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4 | 1, 2, 3 | mp2an 672 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 ax-nul 4532 ax-pr 4642 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-v 3080 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-sn 3989 df-pr 3991 df-altop 28156 |
This theorem is referenced by: altopthd 28170 altopelaltxp 28174 |
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