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Mirrors > Home > ILE Home > Th. List > pm2.65i | Unicode version |
Description: Inference for proof by contradiction. (Contributed by NM, 18-May-1994.) (Proof shortened by Wolf Lammen, 11-Sep-2013.) |
Ref | Expression |
---|---|
pm2.65i.1 |
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pm2.65i.2 |
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Ref | Expression |
---|---|
pm2.65i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.65i.2 |
. . 3
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2 | pm2.65i.1 |
. . 3
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3 | 1, 2 | nsyl3 626 |
. 2
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4 | pm2.01 616 |
. 2
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5 | 3, 4 | ax-mp 5 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-in1 614 ax-in2 615 |
This theorem is referenced by: mt2 640 mto 662 pm5.19 706 noel 3426 0nelop 4248 elirr 4540 en2lp 4553 soirri 5023 canth 5828 0neqopab 5919 fzp1disj 10079 fzonel 10159 fzouzdisj 10179 lgsval2lem 14381 bj-imnimnn 14460 nnnotnotr 14712 |
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