Theorem npcan1

Description: Cancellation law for subtraction and addition with 1. (Contributed by Alexander van der Vekens, 5-Oct-2018)

	Ref	Expression
Assertion	npcan1	⊢ ( 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	npcand	⊢ ( 𝐴 ∈ ℂ → ( ( 𝐴 − 1 ) + 1 ) = 𝐴 )