Theorem pncan1

Description: Cancellation law for addition and subtraction with 1. (Contributed by Alexander van der Vekens, 3-Oct-2018)

	Ref	Expression
Assertion	pncan1	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 + 1 ) − 1 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐴 ∈ ℂ → 𝐴 ∈ ℂ )
2		1cnd	⊢ ( 𝐴 ∈ ℂ → 1 ∈ ℂ )
3	1 2	pncand	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 + 1 ) − 1 ) = 𝐴 )