Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 26-May-1993)
Ref | Expression | ||
---|---|---|---|
Assertion | hbab1 | ⊢ ( 𝑦 ∈ { 𝑥 ∣ 𝜑 } → ∀ 𝑥 𝑦 ∈ { 𝑥 ∣ 𝜑 } ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clab | ⊢ ( 𝑦 ∈ { 𝑥 ∣ 𝜑 } ↔ [ 𝑦 / 𝑥 ] 𝜑 ) | |
2 | hbs1 | ⊢ ( [ 𝑦 / 𝑥 ] 𝜑 → ∀ 𝑥 [ 𝑦 / 𝑥 ] 𝜑 ) | |
3 | 1 2 | hbxfrbi | ⊢ ( 𝑦 ∈ { 𝑥 ∣ 𝜑 } → ∀ 𝑥 𝑦 ∈ { 𝑥 ∣ 𝜑 } ) |