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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 637 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → 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-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm2.62 667 pm2.73 719 pm4.72 736 undif4 3284 |
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