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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > aovnuoveq | Structured version Visualization version Unicode version |
Description: The alternative value of the operation on an ordered pair equals the operation's value at this ordered pair. (Contributed by Alexander van der Vekens, 26-May-2017.) |
Ref | Expression |
---|---|
aovnuoveq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-aov 38710 |
. . 3
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2 | 1 | neeq1i 2688 |
. 2
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3 | afvnufveq 38740 |
. . 3
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4 | df-ov 6279 |
. . 3
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5 | 3, 1, 4 | 3eqtr4g 2511 |
. 2
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6 | 2, 5 | sylbi 200 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-rab 2746 df-v 3015 df-un 3377 df-if 3850 df-fv 5569 df-ov 6279 df-afv 38709 df-aov 38710 |
This theorem is referenced by: (None) |
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