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Mirrors > Home > ILE Home > Th. List > con1dc | Unicode version |
Description: Contraposition for a decidable proposition. Based on theorem *2.15 of [WhiteheadRussell] p. 102. (Contributed by Jim Kingdon, 29-Mar-2018.) |
Ref | Expression |
---|---|
con1dc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 629 |
. . 3
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2 | 1 | imim2i 12 |
. 2
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3 | condc 853 |
. 2
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4 | 2, 3 | syl5 32 |
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-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-stab 831 df-dc 835 |
This theorem is referenced by: impidc 858 simplimdc 860 con1biimdc 873 con1bdc 878 pm3.13dc 959 necon1aidc 2398 necon1bidc 2399 necon1addc 2423 necon1bddc 2424 exmidapne 7258 phiprmpw 12221 fldivp1 12345 prmpwdvds 12352 |
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