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Mirrors > Home > MPE Home > Th. List > stoic2a | Structured version Visualization version GIF version |
Description: Stoic logic Thema 2 version a. Statement T2 of [Bobzien] p. 117 shows a reconstructed version of Stoic logic thema 2 as follows: "When from two assertibles a third follows, and from the third and one (or both) of the two another follows, then this other follows from the first two." Bobzien uses constructs such as 𝜑, 𝜓⊢ 𝜒; in Metamath we will represent that construct as 𝜑 ∧ 𝜓 → 𝜒. This version a is without the phrase "or both"; see stoic2b 1691 for the version with the phrase "or both". We already have this rule as syldan 486, so here we show the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.) |
Ref | Expression |
---|---|
stoic2a.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
stoic2a.2 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
stoic2a | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stoic2a.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | stoic2a.2 | . 2 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | syldan 486 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: (None) |
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