Metamath Proof Explorer


Theorem letrid

Description: Trichotomy law for 'less than or equal to'. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses ltd.1
|- ( ph -> A e. RR )
ltd.2
|- ( ph -> B e. RR )
Assertion letrid
|- ( ph -> ( A <_ B \/ B <_ A ) )

Proof

Step Hyp Ref Expression
1 ltd.1
 |-  ( ph -> A e. RR )
2 ltd.2
 |-  ( ph -> B e. RR )
3 letric
 |-  ( ( A e. RR /\ B e. RR ) -> ( A <_ B \/ B <_ A ) )
4 1 2 3 syl2anc
 |-  ( ph -> ( A <_ B \/ B <_ A ) )