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Mirrors > Home > MPE Home > Th. List > Mathboxes > confun2 | Structured version Visualization version GIF version |
Description: Confun simplified to two propositions. (Contributed by Jarvin Udandy, 6-Sep-2020.) |
Ref | Expression |
---|---|
confun2.1 | ⊢ (𝜓 → 𝜑) |
confun2.2 | ⊢ (𝜓 → ¬ (𝜓 → (𝜓 ∧ ¬ 𝜓))) |
confun2.3 | ⊢ ((𝜓 → 𝜑) → ((𝜓 → 𝜑) → 𝜑)) |
Ref | Expression |
---|---|
confun2 | ⊢ (𝜓 → (¬ (𝜓 → (𝜓 ∧ ¬ 𝜓)) ↔ (𝜓 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | confun2.1 | . 2 ⊢ (𝜓 → 𝜑) | |
2 | confun2.2 | . 2 ⊢ (𝜓 → ¬ (𝜓 → (𝜓 ∧ ¬ 𝜓))) | |
3 | confun2.3 | . 2 ⊢ ((𝜓 → 𝜑) → ((𝜓 → 𝜑) → 𝜑)) | |
4 | 1, 1, 2, 3 | confun 39755 | 1 ⊢ (𝜓 → (¬ (𝜓 → (𝜓 ∧ ¬ 𝜓)) ↔ (𝜓 → 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 195 ∧ wa 383 |
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 196 |
This theorem is referenced by: (None) |
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