New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > anor | GIF version |
Description: Conjunction in terms of disjunction (De Morgan's law). Theorem *4.5 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Nov-2012.) |
Ref | Expression |
---|---|
anor | ⊢ ((φ ∧ ψ) ↔ ¬ (¬ φ ∨ ¬ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ianor 474 | . . 3 ⊢ (¬ (φ ∧ ψ) ↔ (¬ φ ∨ ¬ ψ)) | |
2 | 1 | bicomi 193 | . 2 ⊢ ((¬ φ ∨ ¬ ψ) ↔ ¬ (φ ∧ ψ)) |
3 | 2 | con2bii 322 | 1 ⊢ ((φ ∧ ψ) ↔ ¬ (¬ φ ∨ ¬ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 176 ∨ wo 357 ∧ wa 358 |
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 177 df-or 359 df-an 360 |
This theorem is referenced by: pm3.1 484 pm3.11 485 dn1 932 3anor 948 ltcirr 6272 |
Copyright terms: Public domain | W3C validator |