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Mirrors > Home > MPE Home > Th. List > pm5.21im | Structured version Visualization version GIF version |
Description: Two propositions are equivalent if they are both false. Closed form of 2false 375. Equivalent to a biimpr 219-like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013.) |
Ref | Expression |
---|---|
pm5.21im | ⊢ (¬ 𝜑 → (¬ 𝜓 → (𝜑 ↔ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nbn2 370 | . 2 ⊢ (¬ 𝜑 → (¬ 𝜓 ↔ (𝜑 ↔ 𝜓))) | |
2 | 1 | biimpd 228 | 1 ⊢ (¬ 𝜑 → (¬ 𝜓 → (𝜑 ↔ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 205 |
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 206 |
This theorem is referenced by: pm5.21ndd 380 pm5.21 821 |
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