Theorem naddss2

Description: Ordinal less-than-or-equal is not affected by natural addition. (Contributed by Scott Fenton, 9-Sep-2024)

	Ref	Expression
Assertion	naddss2	Could not format assertion : No typesetting found for |- ( ( A e. On /\ B e. On /\ C e. On ) -> ( A C_ B <-> ( C +no A ) C_ ( C +no B ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		naddss1	Could not format ( ( A e. On /\ B e. On /\ C e. On ) -> ( A C_ B <-> ( A +no C ) C_ ( B +no C ) ) ) : No typesetting found for |- ( ( A e. On /\ B e. On /\ C e. On ) -> ( A C_ B <-> ( A +no C ) C_ ( B +no C ) ) ) with typecode |-
2		naddcom	Could not format ( ( A e. On /\ C e. On ) -> ( A +no C ) = ( C +no A ) ) : No typesetting found for |- ( ( A e. On /\ C e. On ) -> ( A +no C ) = ( C +no A ) ) with typecode |-
3	2	3adant2	Could not format ( ( A e. On /\ B e. On /\ C e. On ) -> ( A +no C ) = ( C +no A ) ) : No typesetting found for |- ( ( A e. On /\ B e. On /\ C e. On ) -> ( A +no C ) = ( C +no A ) ) with typecode |-
4		naddcom	Could not format ( ( B e. On /\ C e. On ) -> ( B +no C ) = ( C +no B ) ) : No typesetting found for |- ( ( B e. On /\ C e. On ) -> ( B +no C ) = ( C +no B ) ) with typecode |-
5	4	3adant1	Could not format ( ( A e. On /\ B e. On /\ C e. On ) -> ( B +no C ) = ( C +no B ) ) : No typesetting found for |- ( ( A e. On /\ B e. On /\ C e. On ) -> ( B +no C ) = ( C +no B ) ) with typecode |-
6	3 5	sseq12d	Could not format ( ( A e. On /\ B e. On /\ C e. On ) -> ( ( A +no C ) C_ ( B +no C ) <-> ( C +no A ) C_ ( C +no B ) ) ) : No typesetting found for |- ( ( A e. On /\ B e. On /\ C e. On ) -> ( ( A +no C ) C_ ( B +no C ) <-> ( C +no A ) C_ ( C +no B ) ) ) with typecode |-
7	1 6	bitrd	Could not format ( ( A e. On /\ B e. On /\ C e. On ) -> ( A C_ B <-> ( C +no A ) C_ ( C +no B ) ) ) : No typesetting found for |- ( ( A e. On /\ B e. On /\ C e. On ) -> ( A C_ B <-> ( C +no A ) C_ ( C +no B ) ) ) with typecode |-