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Mirrors > Home > ILE Home > Th. List > pm3.24 | GIF version |
Description: Law of noncontradiction. Theorem *3.24 of [WhiteheadRussell] p. 111 (who call it the "law of contradiction"). (Contributed by NM, 16-Sep-1993.) (Revised by Mario Carneiro, 2-Feb-2015.) |
Ref | Expression |
---|---|
pm3.24 | ⊢ ¬ (𝜑 ∧ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 591 | . 2 ⊢ (𝜑 → ¬ ¬ 𝜑) | |
2 | imnan 656 | . 2 ⊢ ((𝜑 → ¬ ¬ 𝜑) ↔ ¬ (𝜑 ∧ ¬ 𝜑)) | |
3 | 1, 2 | mpbi 143 | 1 ⊢ ¬ (𝜑 ∧ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 102 |
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 576 ax-in2 577 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: pm4.43 890 excxor 1309 nonconne 2257 dfnul2 3253 dfnul3 3254 rabnc 3277 axnul 3903 zeoxor 10268 nnexmid 10570 |
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