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Mirrors > Home > NFE Home > Th. List > 2falsed | GIF version |
Description: Two falsehoods are equivalent (deduction rule). (Contributed by NM, 11-Oct-2013.) |
Ref | Expression |
---|---|
2falsed.1 | ⊢ (φ → ¬ ψ) |
2falsed.2 | ⊢ (φ → ¬ χ) |
Ref | Expression |
---|---|
2falsed | ⊢ (φ → (ψ ↔ χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2falsed.1 | . . 3 ⊢ (φ → ¬ ψ) | |
2 | 1 | pm2.21d 98 | . 2 ⊢ (φ → (ψ → χ)) |
3 | 2falsed.2 | . . 3 ⊢ (φ → ¬ χ) | |
4 | 3 | pm2.21d 98 | . 2 ⊢ (φ → (χ → ψ)) |
5 | 2, 4 | impbid 183 | 1 ⊢ (φ → (ψ ↔ χ)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 176 |
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 |
This theorem is referenced by: pm5.21ni 341 bianfd 892 abvor0 3567 eqfnfv 5392 |
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