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Mirrors > Home > MPE Home > Th. List > curryax | Structured version Visualization version GIF version |
Description: A non-intuitionistic positive statement, sometimes called a paradox of material implication. Sometimes called Curry's axiom. Similar to exmid 892 (obtained by substituting ⊥ for 𝜓) but positive. For another non-intuitionistic positive statement, see peirce 201. (Contributed by BJ, 4-Apr-2021.) |
Ref | Expression |
---|---|
curryax | ⊢ (𝜑 ∨ (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.21 123 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
2 | 1 | orri 859 | 1 ⊢ (𝜑 ∨ (𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 844 |
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 df-or 845 |
This theorem is referenced by: reuprg 4640 tsim2 36275 |
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