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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm11.12 | Structured version Visualization version GIF version |
Description: Theorem *11.12 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.) |
Ref | Expression |
---|---|
pm11.12 | ⊢ (∀𝑥∀𝑦(𝜑 ∨ 𝜓) → (𝜑 ∨ ∀𝑥∀𝑦𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm10.12 41649 | . . 3 ⊢ (∀𝑦(𝜑 ∨ 𝜓) → (𝜑 ∨ ∀𝑦𝜓)) | |
2 | 1 | alimi 1819 | . 2 ⊢ (∀𝑥∀𝑦(𝜑 ∨ 𝜓) → ∀𝑥(𝜑 ∨ ∀𝑦𝜓)) |
3 | pm10.12 41649 | . 2 ⊢ (∀𝑥(𝜑 ∨ ∀𝑦𝜓) → (𝜑 ∨ ∀𝑥∀𝑦𝜓)) | |
4 | 2, 3 | syl 17 | 1 ⊢ (∀𝑥∀𝑦(𝜑 ∨ 𝜓) → (𝜑 ∨ ∀𝑥∀𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 847 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 |
This theorem depends on definitions: df-bi 210 df-or 848 df-ex 1788 |
This theorem is referenced by: (None) |
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