Theorem pweqd

Description: Equality deduction for power class. (Contributed by NM, 27-Nov-2013)

	Ref	Expression
Hypothesis	pweqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	pweqd	⊢ ( 𝜑 → 𝒫 𝐴 = 𝒫 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		pweqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		pweq	⊢ ( 𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → 𝒫 𝐴 = 𝒫 𝐵 )