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Mirrors > Home > MPE Home > Th. List > pm4.52 | Structured version Visualization version GIF version |
Description: Theorem *4.52 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.) |
Ref | Expression |
---|---|
pm4.52 | ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | annim 407 | . 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓)) | |
2 | imor 853 | . 2 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓)) | |
3 | 1, 2 | xchbinx 337 | 1 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 209 ∧ wa 399 ∨ wo 847 |
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 210 df-an 400 df-or 848 |
This theorem is referenced by: pm4.53 986 ordtri3 6270 ifpim123g 40840 |
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