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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-falor2 | Structured version Visualization version GIF version |
Description: Dual of truan 1553. (Contributed by BJ, 26-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-falor2 | ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | falim 1559 | . . 3 ⊢ (⊥ → 𝜑) | |
2 | 1 | bj-jaoi1 34748 | . 2 ⊢ ((⊥ ∨ 𝜑) → 𝜑) |
3 | olc 865 | . 2 ⊢ (𝜑 → (⊥ ∨ 𝜑)) | |
4 | 2, 3 | impbii 208 | 1 ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∨ wo 844 ⊥wfal 1554 |
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 df-tru 1545 df-fal 1555 |
This theorem is referenced by: (None) |
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