Theorem lep1

Description: A number is less than or equal to itself plus 1. (Contributed by NM, 5-Jan-2006)

	Ref	Expression
Assertion	lep1	|- ( A e. RR -> A <_ ( A + 1 ) )

Proof

Step	Hyp	Ref	Expression
1		ltp1	|- ( A e. RR -> A < ( A + 1 ) )
2		peano2re	|- ( A e. RR -> ( A + 1 ) e. RR )
3		ltle	|- ( ( A e. RR /\ ( A + 1 ) e. RR ) -> ( A < ( A + 1 ) -> A <_ ( A + 1 ) ) )
4	2 3	mpdan	|- ( A e. RR -> ( A < ( A + 1 ) -> A <_ ( A + 1 ) ) )
5	1 4	mpd	|- ( A e. RR -> A <_ ( A + 1 ) )