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Mirrors > Home > MPE Home > Th. List > eqneltrd | Structured version Visualization 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 | |
eqneltrd.2 |
Ref | Expression |
---|---|
eqneltrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqneltrd.2 | . 2 | |
2 | eqneltrd.1 | . . 3 | |
3 | 2 | eleq1d 2686 | . 2 |
4 | 1, 3 | mtbird 315 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wceq 1483 wcel 1990 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-cleq 2615 df-clel 2618 |
This theorem is referenced by: eqneltrrd 2721 opabn1stprc 7228 omopth2 7664 fpwwe2 9465 znnn0nn 11489 sqrtneglem 14007 dvdsaddre2b 15029 mreexmrid 16303 mplcoe1 19465 mplcoe5 19468 2sqn0 29646 reprpmtf1o 30704 fvnobday 31829 bj-snmoore 33068 islln2a 34803 islpln2a 34834 islvol2aN 34878 oddfl 39489 sumnnodd 39862 sinaover2ne0 40079 dvnprodlem1 40161 dirker2re 40309 dirkerdenne0 40310 dirkertrigeqlem3 40317 dirkercncflem1 40320 dirkercncflem2 40321 dirkercncflem4 40323 fouriersw 40448 |
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