Theorem pweqi 3570

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 3569	. 2 |- ( A = B -> ~P A = ~P B )
3	1, 2	ax-mp 5	1 |- ~P A = ~P B

Syntax hints:   = wceq 1348   ~Pcpw 3566

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-in 3127  df-ss 3134  df-pw 3568

This theorem is referenced by:  exmidpw  6886  exmidpweq  6887  pw1dom2  7204  pw1ne1  7206  mnfnre  7962  fmelpw1o  13841