Metamath Proof Explorer


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