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Mirrors > Home > MPE Home > Th. List > norasslem2 | Structured version Visualization version GIF version |
Description: This lemma specializes biimt 364 suitably for the proof of norass 1538. (Contributed by Wolf Lammen, 18-Dec-2023.) |
Ref | Expression |
---|---|
norasslem2 | ⊢ (𝜑 → (𝜓 ↔ ((𝜑 ∨ 𝜒) → 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 866 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒)) | |
2 | biimt 364 | . 2 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ↔ ((𝜑 ∨ 𝜒) → 𝜓))) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝜓 ↔ ((𝜑 ∨ 𝜒) → 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∨ wo 846 |
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 210 df-or 847 |
This theorem is referenced by: norass 1538 |
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