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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nnbist | Unicode version |
Description: If a formula is not
refutable, then it is stable if and only if it is
provable. By double-negation translation, if ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
bj-nnbist |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-stab 817 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | biimpi 119 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | 2 | com12 30 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | bj-trst 13122 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | impbid1 141 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-stab 817 |
This theorem is referenced by: bj-nnbidc 13133 bj-stdc 13137 bj-stst 13139 |
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