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Mirrors > Home > ILE Home > Th. List > pm2.64 | GIF version |
Description: Theorem *2.64 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.64 | ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 5 | . . 3 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → 𝜑)) | |
2 | orel2 645 | . . 3 ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓) → 𝜑)) | |
3 | 1, 2 | jaoi 636 | . 2 ⊢ ((𝜑 ∨ ¬ 𝜓) → ((𝜑 ∨ 𝜓) → 𝜑)) |
4 | 3 | com12 27 | 1 ⊢ ((𝜑 ∨ 𝜓) → ((𝜑 ∨ ¬ 𝜓) → 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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