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Mirrors > Home > ILE Home > Th. List > nf4dc | Unicode version |
Description: Variable is effectively not free in iff is always true or always false, given a decidability condition. The reverse direction, nf4r 1651, holds for all propositions. (Contributed by Jim Kingdon, 21-Jul-2018.) |
Ref | Expression |
---|---|
nf4dc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf2 1648 | . . 3 | |
2 | imordc 883 | . . 3 DECID | |
3 | 1, 2 | syl5bb 191 | . 2 DECID |
4 | orcom 718 | . . 3 | |
5 | alnex 1479 | . . . 4 | |
6 | 5 | orbi2i 752 | . . 3 |
7 | 4, 6 | bitr4i 186 | . 2 |
8 | 3, 7 | bitrdi 195 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 698 DECID wdc 820 wal 1333 wnf 1440 wex 1472 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-gen 1429 ax-ie2 1474 ax-4 1490 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-tru 1338 df-fal 1341 df-nf 1441 |
This theorem is referenced by: (None) |
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