Theorem pweqi 3605

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 3604	. 2 ⊢ (𝐴 = 𝐵 → 𝒫 𝐴 = 𝒫 𝐵)
3	1, 2	ax-mp 5	1 ⊢ 𝒫 𝐴 = 𝒫 𝐵

Syntax hints:   = wceq 1364  𝒫 cpw 3601

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3159  df-ss 3166  df-pw 3603

This theorem is referenced by:  exmidpw  6964  exmidpweq  6965  pw1dom2  7287  pw1ne1  7289  mnfnre  8062  fmelpw1o  15298