Metamath Proof Explorer


Theorem 3cn

Description: The number 3 is a complex number. (Contributed by FL, 17-Oct-2010) Reduce dependencies on axioms. (Revised by Steven Nguyen, 4-Oct-2022)

Ref Expression
Assertion 3cn
|- 3 e. CC

Proof

Step Hyp Ref Expression
1 df-3
 |-  3 = ( 2 + 1 )
2 2cn
 |-  2 e. CC
3 ax-1cn
 |-  1 e. CC
4 2 3 addcli
 |-  ( 2 + 1 ) e. CC
5 1 4 eqeltri
 |-  3 e. CC