Metamath Proof Explorer

Theorem rered

Description: A real number equals its real part. One direction of Proposition 10-3.4(f) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis crred.1 φ A
Assertion rered φ A = A


Step Hyp Ref Expression
1 crred.1 φ A
2 rere A A = A
3 1 2 syl φ A = A