Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > pm4.54 | Structured version Visualization version GIF version |
Description: Theorem *4.54 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.) |
Ref | Expression |
---|---|
pm4.54 | ⊢ ((¬ 𝜑 ∧ 𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-an 400 | . 2 ⊢ ((¬ 𝜑 ∧ 𝜓) ↔ ¬ (¬ 𝜑 → ¬ 𝜓)) | |
2 | pm4.66 849 | . 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 846 |
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 847 |
This theorem is referenced by: pm4.55 987 |
Copyright terms: Public domain | W3C validator |