Metamath Proof Explorer

Theorem ltm1d

Description: A number minus 1 is less than itself. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis ltp1d.1 
|- ( ph -> A e. RR )
Assertion ltm1d 
|- ( ph -> ( A - 1 ) < A )

Proof

Step Hyp Ref Expression
1 ltp1d.1 
 |-  ( ph -> A e. RR )
2 ltm1 
 |-  ( A e. RR -> ( A - 1 ) < A )
3 1 2 syl 
 |-  ( ph -> ( A - 1 ) < A )