Metamath Proof Explorer

Theorem sgnpnf

Description: The signum of +oo is 1. (Contributed by David A. Wheeler, 26-Jun-2016)

Ref Expression
Assertion sgnpnf 
|- ( sgn ` +oo ) = 1

Proof

Step Hyp Ref Expression
1 pnfxr 
 |-  +oo e. RR*
2 0ltpnf 
 |-  0 < +oo
3 sgnp 
 |-  ( ( +oo e. RR* /\ 0 < +oo ) -> ( sgn ` +oo ) = 1 )
4 1 2 3 mp2an 
 |-  ( sgn ` +oo ) = 1