Description: Alternate definition of the class of functions. (Contributed by Peter Mazsa, 30-Aug-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | dffunsALTV2 | ⊢ FunsALTV = { 𝑓 ∈ Rels ∣ ≀ 𝑓 ⊆ I } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffunsALTV | ⊢ FunsALTV = { 𝑓 ∈ Rels ∣ ≀ 𝑓 ∈ CnvRefRels } | |
2 | cosselcnvrefrels2 | ⊢ ( ≀ 𝑓 ∈ CnvRefRels ↔ ( ≀ 𝑓 ⊆ I ∧ ≀ 𝑓 ∈ Rels ) ) | |
3 | cosselrels | ⊢ ( 𝑓 ∈ Rels → ≀ 𝑓 ∈ Rels ) | |
4 | 3 | biantrud | ⊢ ( 𝑓 ∈ Rels → ( ≀ 𝑓 ⊆ I ↔ ( ≀ 𝑓 ⊆ I ∧ ≀ 𝑓 ∈ Rels ) ) ) |
5 | 2 4 | bitr4id | ⊢ ( 𝑓 ∈ Rels → ( ≀ 𝑓 ∈ CnvRefRels ↔ ≀ 𝑓 ⊆ I ) ) |
6 | 1 5 | rabimbieq | ⊢ FunsALTV = { 𝑓 ∈ Rels ∣ ≀ 𝑓 ⊆ I } |