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Mirrors > Home > ILE Home > Th. List > pm2.21fal | Unicode version |
Description: If a wff and its negation are provable, then falsum is provable. (Contributed by Mario Carneiro, 9-Feb-2017.) |
Ref | Expression |
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pm2.21fal.1 | |
pm2.21fal.2 |
Ref | Expression |
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pm2.21fal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21fal.1 | . 2 | |
2 | pm2.21fal.2 | . 2 | |
3 | 1, 2 | pm2.21dd 610 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wfal 1347 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-in2 605 |
This theorem is referenced by: genpdisj 7455 suplocexprlemdisj 7652 suplocexprlemub 7655 suplocsrlem 7740 recvguniqlem 10922 resqrexlemoverl 10949 leabs 11002 climge0 11252 isprm5lem 12052 dedekindeulemeu 13147 dedekindicclemeu 13156 pw1nct 13724 |
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