Description: Equivalent wff's yield equal restricted class abstractions. (Contributed by Glauco Siliprandi, 26-Jun-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | rabbia2.1 | ⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) ↔ ( 𝑥 ∈ 𝐵 ∧ 𝜒 ) ) | |
Assertion | rabbia2 | ⊢ { 𝑥 ∈ 𝐴 ∣ 𝜓 } = { 𝑥 ∈ 𝐵 ∣ 𝜒 } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabbia2.1 | ⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) ↔ ( 𝑥 ∈ 𝐵 ∧ 𝜒 ) ) | |
2 | 1 | a1i | ⊢ ( ⊤ → ( ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) ↔ ( 𝑥 ∈ 𝐵 ∧ 𝜒 ) ) ) |
3 | 2 | rabbidva2 | ⊢ ( ⊤ → { 𝑥 ∈ 𝐴 ∣ 𝜓 } = { 𝑥 ∈ 𝐵 ∣ 𝜒 } ) |
4 | 3 | mptru | ⊢ { 𝑥 ∈ 𝐴 ∣ 𝜓 } = { 𝑥 ∈ 𝐵 ∣ 𝜒 } |