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Mirrors > Home > ILE Home > Th. List > pm5.19 | GIF version |
Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm5.19 | ⊢ ¬ (𝜑 ↔ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 116 | . . . 4 ⊢ ((𝜑 ↔ ¬ 𝜑) → (𝜑 → ¬ 𝜑)) | |
2 | 1 | pm2.01d 583 | . . 3 ⊢ ((𝜑 ↔ ¬ 𝜑) → ¬ 𝜑) |
3 | id 19 | . . 3 ⊢ ((𝜑 ↔ ¬ 𝜑) → (𝜑 ↔ ¬ 𝜑)) | |
4 | 2, 3 | mpbird 165 | . 2 ⊢ ((𝜑 ↔ ¬ 𝜑) → 𝜑) |
5 | 4, 2 | pm2.65i 603 | 1 ⊢ ¬ (𝜑 ↔ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: pm5.16 773 pclem6 1310 pm5.18im 1321 ru 2839 |
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