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Theorem frege106d 36865
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 37082. (Contributed by RP, 15-Jul-2020.)
Hypothesis
Ref Expression
frege106d.cb (𝜑𝐴𝑅𝐵)
Assertion
Ref Expression
frege106d (𝜑 → (𝐴𝑅𝐵𝐴 = 𝐵))

Proof of Theorem frege106d
StepHypRef Expression
1 frege106d.cb . 2 (𝜑𝐴𝑅𝐵)
21orcd 405 1 (𝜑 → (𝐴𝑅𝐵𝐴 = 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 381   = wceq 1474   class class class wbr 4573
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 195  df-or 383
This theorem is referenced by:  frege108d  36866
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