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Mirrors > Home > NFE Home > Th. List > ninba | GIF version |
Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.) |
Ref | Expression |
---|---|
ninba.1 | ⊢ φ |
Ref | Expression |
---|---|
ninba | ⊢ (¬ ψ → (¬ φ ↔ (χ ∧ ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ninba.1 | . . 3 ⊢ φ | |
2 | 1 | niabn 917 | . 2 ⊢ (¬ ψ → ((χ ∧ ψ) ↔ ¬ φ)) |
3 | 2 | bicomd 192 | 1 ⊢ (¬ ψ → (¬ φ ↔ (χ ∧ ψ))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 176 ∧ wa 358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: (None) |
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