Theorem rngoiso1o

Description: A ring isomorphism is a bijection. (Contributed by Jeff Madsen, 16-Jun-2011)

	Ref	Expression
Hypotheses	rngisoval.1	$$⊢G=1^{st}\left(R\right)$$
	rngisoval.2	$$⊢X=\mathrm{ran}G$$
	rngisoval.3	$$⊢J=1^{st}\left(S\right)$$
	rngisoval.4	$$⊢Y=\mathrm{ran}J$$
Assertion	rngoiso1o	Could not format assertion : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps /\ F e. ( R RingOpsIso S ) ) -> F : X -1-1-onto-> Y ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		rngisoval.1	$$⊢G=1^{st}\left(R\right)$$
2		rngisoval.2	$$⊢X=\mathrm{ran}G$$
3		rngisoval.3	$$⊢J=1^{st}\left(S\right)$$
4		rngisoval.4	$$⊢Y=\mathrm{ran}J$$
5	1 2 3 4	isrngoiso	Could not format ( ( R e. RingOps /\ S e. RingOps ) -> ( F e. ( R RingOpsIso S ) <-> ( F e. ( R RingOpsHom S ) /\ F : X -1-1-onto-> Y ) ) ) : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps ) -> ( F e. ( R RingOpsIso S ) <-> ( F e. ( R RingOpsHom S ) /\ F : X -1-1-onto-> Y ) ) ) with typecode |-
6	5	simplbda	Could not format ( ( ( R e. RingOps /\ S e. RingOps ) /\ F e. ( R RingOpsIso S ) ) -> F : X -1-1-onto-> Y ) : No typesetting found for |- ( ( ( R e. RingOps /\ S e. RingOps ) /\ F e. ( R RingOpsIso S ) ) -> F : X -1-1-onto-> Y ) with typecode |-
7	6	3impa	Could not format ( ( R e. RingOps /\ S e. RingOps /\ F e. ( R RingOpsIso S ) ) -> F : X -1-1-onto-> Y ) : No typesetting found for |- ( ( R e. RingOps /\ S e. RingOps /\ F e. ( R RingOpsIso S ) ) -> F : X -1-1-onto-> Y ) with typecode |-