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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nnan | Unicode version |
Description: The double negation of a conjunction implies the conjunction of the double negations. (Contributed by BJ, 24-Nov-2023.) |
Ref | Expression |
---|---|
bj-nnan |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . . . 4 | |
2 | 1 | con3i 627 | . . 3 |
3 | 2 | con3i 627 | . 2 |
4 | simpr 109 | . . . 4 | |
5 | 4 | con3i 627 | . . 3 |
6 | 5 | con3i 627 | . 2 |
7 | 3, 6 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 |
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 609 ax-in2 610 |
This theorem is referenced by: bj-stan 13741 bj-stand 13742 |
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