Theorem pweqALT

Description: Alternate proof of pweq directly from the definition. (Contributed by NM, 21-Jun-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	pweqALT	|- ( A = B -> ~P A = ~P B )

Proof

Step	Hyp	Ref	Expression
1		sseq2	|- ( A = B -> ( x C_ A <-> x C_ B ) )
2	1	abbidv	|- ( A = B -> { x | x C_ A } = { x | x C_ B } )
3		df-pw	|- ~P A = { x | x C_ A }
4		df-pw	|- ~P B = { x | x C_ B }
5	2 3 4	3eqtr4g	|- ( A = B -> ~P A = ~P B )