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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 | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 629 | . . 3 | |
2 | 1 | imim2i 12 | . 2 |
3 | condc 853 | . 2 DECID | |
4 | 2, 3 | syl5 32 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 DECID wdc 834 |
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 2396 necon1bidc 2397 necon1addc 2421 necon1bddc 2422 phiprmpw 12188 fldivp1 12312 prmpwdvds 12319 |
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