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Mirrors > Home > ILE Home > Th. List > nbn3 | GIF version |
Description: Transfer falsehood via equivalence. (Contributed by NM, 11-Sep-2006.) |
Ref | Expression |
---|---|
nbn3.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
nbn3 | ⊢ (¬ 𝜓 ↔ (𝜓 ↔ ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nbn3.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | notnoti 645 | . 2 ⊢ ¬ ¬ 𝜑 |
3 | 2 | nbn 699 | 1 ⊢ (¬ 𝜓 ↔ (𝜓 ↔ ¬ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 105 |
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 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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