Metamath Proof Explorer


Theorem prstcle

Description: Value of the less-than-or-equal-to relation is unchanged. (Contributed by Zhi Wang, 20-Sep-2024)

Ref Expression
Hypotheses prstcnid.c No typesetting found for |- ( ph -> C = ( ProsetToCat ` K ) ) with typecode |-
prstcnid.k φKProset
prstcle.l φ˙=K
Assertion prstcle φX˙YXCY

Proof

Step Hyp Ref Expression
1 prstcnid.c Could not format ( ph -> C = ( ProsetToCat ` K ) ) : No typesetting found for |- ( ph -> C = ( ProsetToCat ` K ) ) with typecode |-
2 prstcnid.k φKProset
3 prstcle.l φ˙=K
4 1 2 3 prstcleval φ˙=C
5 4 breqd φX˙YXCY