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Mirrors > Home > ILE Home > Th. List > biort | GIF version |
Description: A wff is disjoined with truth is true. (Contributed by NM, 23-May-1999.) |
Ref | Expression |
---|---|
biort | ⊢ (𝜑 → (𝜑 ↔ (𝜑 ∨ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 665 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓)) | |
2 | ax-1 5 | . 2 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → 𝜑)) | |
3 | 1, 2 | impbid2 141 | 1 ⊢ (𝜑 → (𝜑 ↔ (𝜑 ∨ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 103 ∨ wo 661 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: pm5.55dc 852 |
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