Metamath Proof Explorer


Theorem 5olt9o

Description: Ordinal 5 is less than ordinal 9. (Contributed by BTernaryTau, 17-Oct-2026)

Ref Expression
Assertion 5olt9o Could not format assertion : No typesetting found for |- 5o e. 9o with typecode |-

Proof

Step Hyp Ref Expression
1 5on Could not format 5o e. On : No typesetting found for |- 5o e. On with typecode |-
2 sucidg Could not format ( 5o e. On -> 5o e. suc 5o ) : No typesetting found for |- ( 5o e. On -> 5o e. suc 5o ) with typecode |-
3 1 2 ax-mp Could not format 5o e. suc 5o : No typesetting found for |- 5o e. suc 5o with typecode |-
4 df-6o Could not format 6o = suc 5o : No typesetting found for |- 6o = suc 5o with typecode |-
5 3 4 eleqtrri Could not format 5o e. 6o : No typesetting found for |- 5o e. 6o with typecode |-
6 6olt9o Could not format 6o e. 9o : No typesetting found for |- 6o e. 9o with typecode |-
7 9on Could not format 9o e. On : No typesetting found for |- 9o e. On with typecode |-
8 ontr1 Could not format ( 9o e. On -> ( ( 5o e. 6o /\ 6o e. 9o ) -> 5o e. 9o ) ) : No typesetting found for |- ( 9o e. On -> ( ( 5o e. 6o /\ 6o e. 9o ) -> 5o e. 9o ) ) with typecode |-
9 7 8 ax-mp Could not format ( ( 5o e. 6o /\ 6o e. 9o ) -> 5o e. 9o ) : No typesetting found for |- ( ( 5o e. 6o /\ 6o e. 9o ) -> 5o e. 9o ) with typecode |-
10 5 6 9 mp2an Could not format 5o e. 9o : No typesetting found for |- 5o e. 9o with typecode |-