Theorem pweqi 3660

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

Hypothesis

Ref	Expression
pweqi.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
pweqi	⊢ 𝒫 𝐴 = 𝒫 𝐵

Proof of Theorem pweqi

Step	Hyp	Ref	Expression
1		pweqi.1	. 2 ⊢ 𝐴 = 𝐵
2		pweq 3659	. 2 ⊢ (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
3	1, 2	ax-mp 5	1 ⊢ 𝒫 𝐴 = 𝒫 𝐵

Syntax hints:   = wceq 1398  𝒫 cpw 3656

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3207  df-ss 3214  df-pw 3658

This theorem is referenced by:  exmidpw  7143  exmidpweq  7144  pw1dom2  7488  pw1ne1  7490  mnfnre  8264  umgrpredgv  16071  issubgr  16181  uhgrissubgr  16185  konigsbergiedgwen  16408