Theorem opprnzr

Description: The opposite of a nonzero ring is nonzero. (Contributed by Mario Carneiro, 17-Jun-2015)

	Ref	Expression
Hypothesis	opprnzr.1	|- O = ( oppR ` R )
Assertion	opprnzr	|- ( R e. NzRing -> O e. NzRing )

Proof

Step	Hyp	Ref	Expression
1		opprnzr.1	|- O = ( oppR ` R )
2	1	opprnzrb	|- ( R e. NzRing <-> O e. NzRing )
3	2	biimpi	|- ( R e. NzRing -> O e. NzRing )