Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > pm4.65 | Structured version Visualization version GIF version |
Description: Theorem *4.65 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.65 | ⊢ (¬ (¬ 𝜑 → 𝜓) ↔ (¬ 𝜑 ∧ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.61 408 | 1 ⊢ (¬ (¬ 𝜑 → 𝜓) ↔ (¬ 𝜑 ∧ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 209 ∧ wa 399 |
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 |
This theorem is referenced by: ioran 984 |
Copyright terms: Public domain | W3C validator |