Theorem pweqi 3620

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 3619	. 2 |- ( A = B -> ~P A = ~P B )
3	1, 2	ax-mp 5	1 |- ~P A = ~P B

Syntax hints:   = wceq 1373   ~Pcpw 3616

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-pw 3618

This theorem is referenced by:  exmidpw  7007  exmidpweq  7008  pw1dom2  7341  pw1ne1  7343  mnfnre  8117  fmelpw1o  15779