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Mirrors > Home > MPE Home > Th. List > pm4.64 | Structured version Visualization version GIF version |
Description: Theorem *4.64 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.64 | ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-or 847 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
2 | 1 | bicomi 227 | 1 ⊢ ((¬ 𝜑 → 𝜓) ↔ (𝜑 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 209 ∨ 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-or 847 |
This theorem is referenced by: pm4.66 849 ioran 983 dfifp3 1065 fimaxg 8839 fiming 9035 kmlem8 9657 axgroth6 10328 dfconn2 22170 ifpimimb 40665 ifpor123g 40669 hirstL-ax3 43926 |
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