Theorem frege106d

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 . (Contributed by RP, 15-Jul-2020)

	Ref	Expression
Hypothesis	frege106d.cb	⊢ ( 𝜑 → 𝐴 𝑅 𝐵 )
Assertion	frege106d	⊢ ( 𝜑 → ( 𝐴 𝑅 𝐵 ∨ 𝐴 = 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		frege106d.cb	⊢ ( 𝜑 → 𝐴 𝑅 𝐵 )
2	1	orcd	⊢ ( 𝜑 → ( 𝐴 𝑅 𝐵 ∨ 𝐴 = 𝐵 ) )