Metamath Proof Explorer


Theorem 6olt9o

Description: Ordinal 6 is less than ordinal 9. (Contributed by BTernaryTau, 17-Oct-2026)

Ref Expression
Assertion 6olt9o Could not format assertion : No typesetting found for |- 6o e. 9o with typecode |-

Proof

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