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Mirrors > Home > MPE Home > Th. List > biorfiOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of biorfi 422 as of 16-Jul-2021. (Contributed by NM, 23-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
biorfi.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
biorfiOLD | ⊢ (𝜓 ↔ (𝜓 ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biorfi.1 | . 2 ⊢ ¬ 𝜑 | |
2 | orc 400 | . . 3 ⊢ (𝜓 → (𝜓 ∨ 𝜑)) | |
3 | orel2 398 | . . 3 ⊢ (¬ 𝜑 → ((𝜓 ∨ 𝜑) → 𝜓)) | |
4 | 2, 3 | impbid2 216 | . 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜓 ∨ 𝜑))) |
5 | 1, 4 | ax-mp 5 | 1 ⊢ (𝜓 ↔ (𝜓 ∨ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 196 ∨ wo 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 197 df-or 385 |
This theorem is referenced by: (None) |
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