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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ovn0dmfun | Structured version Visualization version Unicode version |
Description: If a class' operation value for two operands is not the empty set, the operands are contained in the domain of the class, and the class restricted to the operands is a function, analogous to fvfundmfvn0 5880. (Contributed by AV, 27-Jan-2020.) |
Ref | Expression |
---|---|
ovn0dmfun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 6279 |
. . 3
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2 | 1 | neeq1i 2688 |
. 2
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3 | fvfundmfvn0 5880 |
. 2
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4 | 2, 3 | 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-8 1893 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pow 4554 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3015 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-sn 3937 df-pr 3939 df-op 3943 df-uni 4169 df-br 4375 df-opab 4434 df-id 4727 df-xp 4818 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-res 4824 df-iota 5525 df-fun 5563 df-fv 5569 df-ov 6279 |
This theorem is referenced by: (None) |
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