Theorem abs00i

Description: The absolute value of a number is zero iff the number is zero. Proposition 10-3.7(c) of Gleason p. 133. (Contributed by NM, 28-Jul-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	|- A e. CC
Assertion	abs00i	|- ( ( abs ` A ) = 0 <-> A = 0 )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	|- A e. CC
2		abs00	|- ( A e. CC -> ( ( abs ` A ) = 0 <-> A = 0 ) )
3	1 2	ax-mp	|- ( ( abs ` A ) = 0 <-> A = 0 )