Metamath Proof Explorer


Theorem right1s

Description: The right set of 1s is empty . (Contributed by Scott Fenton, 4-Feb-2025)

Ref Expression
Assertion right1s Could not format assertion : No typesetting found for |- ( _Right ` 1s ) = (/) with typecode |-

Proof

Step Hyp Ref Expression
1 rightval Could not format ( _Right ` 1s ) = { x e. ( _Old ` ( bday ` 1s ) ) | 1s
2 bday1s Could not format ( bday ` 1s ) = 1o : No typesetting found for |- ( bday ` 1s ) = 1o with typecode |-
3 2 fveq2i Could not format ( _Old ` ( bday ` 1s ) ) = ( _Old ` 1o ) : No typesetting found for |- ( _Old ` ( bday ` 1s ) ) = ( _Old ` 1o ) with typecode |-
4 old1 Could not format ( _Old ` 1o ) = { 0s } : No typesetting found for |- ( _Old ` 1o ) = { 0s } with typecode |-
5 3 4 eqtri Could not format ( _Old ` ( bday ` 1s ) ) = { 0s } : No typesetting found for |- ( _Old ` ( bday ` 1s ) ) = { 0s } with typecode |-
6 5 rabeqi Could not format { x e. ( _Old ` ( bday ` 1s ) ) | 1s
7 breq2 Could not format ( x = 0s -> ( 1s 1s ( 1s 1s
8 7 rabsnif Could not format { x e. { 0s } | 1s
9 6 8 eqtri Could not format { x e. ( _Old ` ( bday ` 1s ) ) | 1s
10 0slt1s Could not format 0s
11 0sno Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
12 1sno Could not format 1s e. No : No typesetting found for |- 1s e. No with typecode |-
13 sltasym Could not format ( ( 0s e. No /\ 1s e. No ) -> ( 0s -. 1s ( 0s -. 1s
14 11 12 13 mp2an Could not format ( 0s -. 1s -. 1s
15 10 14 ax-mp Could not format -. 1s
16 15 iffalsei Could not format if ( 1s
17 1 9 16 3eqtri Could not format ( _Right ` 1s ) = (/) : No typesetting found for |- ( _Right ` 1s ) = (/) with typecode |-