Theorem frege106d 38047

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 38263. (Contributed by RP, 15-Jul-2020.)

Hypothesis

Ref	Expression
frege106d.cb	|- ( ph -> A R B )

Assertion

Ref	Expression
frege106d	|- ( ph -> ( A R B \/ A = B ) )

Proof of Theorem frege106d

Step	Hyp	Ref	Expression
1		frege106d.cb	. 2 |- ( ph -> A R B )
2	1	orcd 407	1 |- ( ph -> ( A R B \/ A = B ) )

Syntax hints:   -> wi 4   \/ wo 383   = wceq 1483   class class class wbr 4653

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 197  df-or 385

This theorem is referenced by:  frege108d  38048