Metamath Proof Explorer


Theorem rerebd

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

Ref Expression
Hypotheses recld.1 φA
rerebd.2 φA=A
Assertion rerebd φA

Proof

Step Hyp Ref Expression
1 recld.1 φA
2 rerebd.2 φA=A
3 rereb AAA=A
4 1 3 syl φAA=A
5 2 4 mpbird φA