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Metamath Proof Explorer
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 ) |