Theorem pweqi 3653

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 3652	. 2 |- ( A = B -> ~P A = ~P B )
3	1, 2	ax-mp 5	1 |- ~P A = ~P B

Syntax hints:   = wceq 1395   ~Pcpw 3649

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3203  df-ss 3210  df-pw 3651

This theorem is referenced by:  exmidpw  7070  exmidpweq  7071  pw1dom2  7412  pw1ne1  7414  fmelpw1o  7432  mnfnre  8189  umgrpredgv  15945