Metamath Proof Explorer


Theorem 1mhlfehlf

Description: Prove that 1 - 1/2 = 1/2. (Contributed by David A. Wheeler, 4-Jan-2017) (Proof shortened by SN, 22-Oct-2025)

Ref Expression
Assertion 1mhlfehlf ( 1 − ( 1 / 2 ) ) = ( 1 / 2 )

Proof

Step Hyp Ref Expression
1 ax-1cn 1 ∈ ℂ
2 halfcn ( 1 / 2 ) ∈ ℂ
3 2halves ( 1 ∈ ℂ → ( ( 1 / 2 ) + ( 1 / 2 ) ) = 1 )
4 1 3 ax-mp ( ( 1 / 2 ) + ( 1 / 2 ) ) = 1
5 1 2 2 4 subaddrii ( 1 − ( 1 / 2 ) ) = ( 1 / 2 )