Description: The fixpoints of a class are a subset of its range. (Contributed by Scott Fenton, 16-Apr-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | fixssrn | ⊢ Fix 𝐴 ⊆ ran 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffix2 | ⊢ Fix 𝐴 = ran ( 𝐴 ∩ I ) | |
2 | inss1 | ⊢ ( 𝐴 ∩ I ) ⊆ 𝐴 | |
3 | 2 | rnssi | ⊢ ran ( 𝐴 ∩ I ) ⊆ ran 𝐴 |
4 | 1 3 | eqsstri | ⊢ Fix 𝐴 ⊆ ran 𝐴 |