Theorem releabsi

Description: The real part of a number is less than or equal to its absolute value. Proposition 10-3.7(d) of Gleason p. 133. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	$$⊢A\in ℂ$$
Assertion	releabsi	$$⊢\Re \left(A\right)\le \left|A\right|$$

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	$$⊢A\in ℂ$$
2		releabs	$$⊢A\in ℂ\to \Re \left(A\right)\le \left|A\right|$$
3	1 2	ax-mp	$$⊢\Re \left(A\right)\le \left|A\right|$$