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Mirrors > Home > MPE Home > Th. List > nss | Structured version Visualization version Unicode version |
Description: Negation of subclass relationship. Exercise 13 of [TakeutiZaring] p. 18. (Contributed by NM, 25-Feb-1996.) (Proof shortened by Andrew Salmon, 21-Jun-2011.) |
Ref | Expression |
---|---|
nss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exanali 1720 |
. . 3
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2 | dfss2 3420 |
. . 3
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3 | 1, 2 | xchbinxr 313 |
. 2
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4 | 3 | bicomi 206 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-in 3410 df-ss 3417 |
This theorem is referenced by: grur1 9242 psslinpr 9453 reclem2pr 9470 mreexexlem2d 15544 prmcyg 17521 filcon 20891 alexsubALTlem4 21058 wilthlem2 23987 shne0i 27094 erdszelem10 29916 fundmpss 30400 relintabex 36181 |
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