Theorem negsf1o

Description: Surreal negation is a bijection. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Assertion	negsf1o	Could not format assertion : No typesetting found for |- -us : No -1-1-onto-> No with typecode |-

Proof

Step	Hyp	Ref	Expression
1		negsf	Could not format -us : No --> No : No typesetting found for |- -us : No --> No with typecode |-
2		negs11	Could not format ( ( x e. No /\ y e. No ) -> ( ( -us ` x ) = ( -us ` y ) <-> x = y ) ) : No typesetting found for |- ( ( x e. No /\ y e. No ) -> ( ( -us ` x ) = ( -us ` y ) <-> x = y ) ) with typecode |-
3	2	biimpd	Could not format ( ( x e. No /\ y e. No ) -> ( ( -us ` x ) = ( -us ` y ) -> x = y ) ) : No typesetting found for |- ( ( x e. No /\ y e. No ) -> ( ( -us ` x ) = ( -us ` y ) -> x = y ) ) with typecode |-
4	3	rgen2	Could not format A. x e. No A. y e. No ( ( -us ` x ) = ( -us ` y ) -> x = y ) : No typesetting found for |- A. x e. No A. y e. No ( ( -us ` x ) = ( -us ` y ) -> x = y ) with typecode |-
5		dff13	Could not format ( -us : No -1-1-> No <-> ( -us : No --> No /\ A. x e. No A. y e. No ( ( -us ` x ) = ( -us ` y ) -> x = y ) ) ) : No typesetting found for |- ( -us : No -1-1-> No <-> ( -us : No --> No /\ A. x e. No A. y e. No ( ( -us ` x ) = ( -us ` y ) -> x = y ) ) ) with typecode |-
6	1 4 5	mpbir2an	Could not format -us : No -1-1-> No : No typesetting found for |- -us : No -1-1-> No with typecode |-
7		negsfo	Could not format -us : No -onto-> No : No typesetting found for |- -us : No -onto-> No with typecode |-
8		df-f1o	Could not format ( -us : No -1-1-onto-> No <-> ( -us : No -1-1-> No /\ -us : No -onto-> No ) ) : No typesetting found for |- ( -us : No -1-1-onto-> No <-> ( -us : No -1-1-> No /\ -us : No -onto-> No ) ) with typecode |-
9	6 7 8	mpbir2an	Could not format -us : No -1-1-onto-> No : No typesetting found for |- -us : No -1-1-onto-> No with typecode |-