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Mirrors > Home > MPE Home > Th. List > nornotOLD | Structured version Visualization version GIF version |
Description: Obsolete version of nornot 1530 as of 8-Dec-2023. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nornotOLD | ⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.56 989 | . 2 ⊢ ((¬ 𝜑 ∧ ¬ 𝜑) ↔ ¬ (𝜑 ∨ 𝜑)) | |
2 | pm4.24 567 | . 2 ⊢ (¬ 𝜑 ↔ (¬ 𝜑 ∧ ¬ 𝜑)) | |
3 | df-nor 1527 | . 2 ⊢ ((𝜑 ⊽ 𝜑) ↔ ¬ (𝜑 ∨ 𝜑)) | |
4 | 1, 2, 3 | 3bitr4i 306 | 1 ⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ∧ wa 399 ∨ wo 847 ⊽ wnor 1526 |
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 df-nor 1527 |
This theorem is referenced by: (None) |
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