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Mirrors > Home > MPE Home > Th. List > pm4.55 | Structured version Visualization version GIF version |
Description: Theorem *4.55 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.55 | ⊢ (¬ (¬ 𝜑 ∧ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.54 983 | . . 3 ⊢ ((¬ 𝜑 ∧ 𝜓) ↔ ¬ (𝜑 ∨ ¬ 𝜓)) | |
2 | 1 | con2bii 360 | . 2 ⊢ ((𝜑 ∨ ¬ 𝜓) ↔ ¬ (¬ 𝜑 ∧ 𝜓)) |
3 | 2 | bicomi 226 | 1 ⊢ (¬ (¬ 𝜑 ∧ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 ∧ wa 398 ∨ wo 843 |
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 209 df-an 399 df-or 844 |
This theorem is referenced by: chrelat2i 30144 hlrelat2 36541 ifpnot23 39851 |
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