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Mirrors > Home > MPE Home > Th. List > eqneltrd | Structured version Unicode version |
Description: If a class is not an element of another class, an equal class is also not an element. Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
eqneltrd.1 |
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eqneltrd.2 |
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Ref | Expression |
---|---|
eqneltrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqneltrd.2 |
. 2
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2 | eqneltrd.1 |
. . 3
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3 | 2 | eleq1d 2519 |
. 2
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4 | 1, 3 | mtbird 301 |
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-12 1794 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-an 371 df-ex 1588 df-cleq 2443 df-clel 2446 |
This theorem is referenced by: eqneltrrd 2559 omopth2 7120 fpwwe2 8908 sqrneglem 12855 mreexmrid 14680 mplcoe1 17648 mplcoe5 17652 mplcoe2OLD 17654 islln2a 33464 islpln2a 33495 islvol2aN 33539 |
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