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Mirrors > Home > MPE Home > Th. List > biortn | Structured version Visualization version GIF version |
Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.) |
Ref | Expression |
---|---|
biortn | ⊢ (𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notnot 144 | . 2 ⊢ (𝜑 → ¬ ¬ 𝜑) | |
2 | biorf 933 | . 2 ⊢ (¬ ¬ 𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓))) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 208 ∨ 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-or 844 |
This theorem is referenced by: oranabs 996 xrdifh 30505 ballotlemfc0 31752 ballotlemfcc 31753 topdifinfindis 34629 topdifinffinlem 34630 4atlem3a 36735 4atlem3b 36736 ntrneineine1lem 40441 |
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