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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-biorfi | Structured version Visualization version GIF version |
Description: This should be labeled "biorfi" while the current biorfi 422 should be labeled "biorfri". The dual of biorf 420 is not biantr 972 but iba 524 (and ibar 525). So there should also be a "biorfr". (Note that these four statements can actually be strengthened to biconditionals.) (Contributed by BJ, 26-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-biorfi.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
bj-biorfi | ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-biorfi.1 | . 2 ⊢ ¬ 𝜑 | |
2 | biorf 420 | . 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜓 ↔ (𝜑 ∨ 𝜓)) |
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: bj-falor 32569 |
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