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Mirrors > Home > ILE Home > Th. List > pm2.621 | GIF version |
Description: Theorem *2.621 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 13-Dec-2013.) |
Ref | Expression |
---|---|
pm2.621 | ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓)) | |
2 | idd 21 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜓 → 𝜓)) | |
3 | 1, 2 | jaod 712 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 703 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: pm2.62 743 pm2.73 801 pm4.72 822 undif4 3476 |
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