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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege106d | Structured version Visualization version GIF version |
Description: If 𝐵 follows 𝐴 in 𝑅, then either 𝐴 and 𝐵 are the same or 𝐵 follows 𝐴 in 𝑅. Similar to Proposition 106 of [Frege1879] p. 73. Compare with frege106 41537. (Contributed by RP, 15-Jul-2020.) |
Ref | Expression |
---|---|
frege106d.cb | ⊢ (𝜑 → 𝐴𝑅𝐵) |
Ref | Expression |
---|---|
frege106d | ⊢ (𝜑 → (𝐴𝑅𝐵 ∨ 𝐴 = 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege106d.cb | . 2 ⊢ (𝜑 → 𝐴𝑅𝐵) | |
2 | 1 | orcd 870 | 1 ⊢ (𝜑 → (𝐴𝑅𝐵 ∨ 𝐴 = 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 844 = wceq 1539 class class class wbr 5075 |
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 206 df-or 845 |
This theorem is referenced by: frege108d 41324 |
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