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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm10.12 | Structured version Visualization version GIF version |
Description: Theorem *10.12 in [WhiteheadRussell] p. 146. In *10, this is treated as an axiom, and the proofs in *10 are based on this theorem. (Contributed by Andrew Salmon, 17-Jun-2011.) |
Ref | Expression |
---|---|
pm10.12 | ⊢ (∀𝑥(𝜑 ∨ 𝜓) → (𝜑 ∨ ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.32v 1947 | . 2 ⊢ (∀𝑥(𝜑 ∨ 𝜓) ↔ (𝜑 ∨ ∀𝑥𝜓)) | |
2 | 1 | biimpi 219 | 1 ⊢ (∀𝑥(𝜑 ∨ 𝜓) → (𝜑 ∨ ∀𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 846 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 |
This theorem depends on definitions: df-bi 210 df-or 847 df-ex 1787 |
This theorem is referenced by: pm11.12 41571 |
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