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Mirrors > Home > MPE Home > Th. List > dedtOLD | Structured version Visualization version GIF version |
Description: Old version of dedt 1031. Obsolete as of 16-Mar-2021. (Contributed by NM, 26-Jun-2002.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dedtOLD.1 | ⊢ ((𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜃 ↔ 𝜏)) |
dedtOLD.2 | ⊢ 𝜏 |
Ref | Expression |
---|---|
dedtOLD | ⊢ (𝜒 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedlema 1002 | . 2 ⊢ (𝜒 → (𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒)))) | |
2 | dedtOLD.2 | . . 3 ⊢ 𝜏 | |
3 | dedtOLD.1 | . . 3 ⊢ ((𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → (𝜃 ↔ 𝜏)) | |
4 | 2, 3 | mpbiri 248 | . 2 ⊢ ((𝜑 ↔ ((𝜑 ∧ 𝜒) ∨ (𝜓 ∧ ¬ 𝜒))) → 𝜃) |
5 | 1, 4 | syl 17 | 1 ⊢ (𝜒 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 196 ∨ wo 383 ∧ wa 384 |
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 df-an 386 |
This theorem is referenced by: con3OLD 1035 |
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