Metamath Proof Explorer


Theorem 4cn

Description: The number 4 is a complex number. (Contributed by David A. Wheeler, 7-Jul-2016) Reduce dependencies on axioms. (Revised by Steven Nguyen, 4-Oct-2022)

Ref Expression
Assertion 4cn
|- 4 e. CC

Proof

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