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| Mirrors > Home > MPE Home > Th. List > rabbii | Structured version Visualization version GIF version | ||
| Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv 3444. (Contributed by Peter Mazsa, 1-Nov-2019.) |
| Ref | Expression |
|---|---|
| rabbii.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| rabbii | ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∈ 𝐴 ∣ 𝜓} |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rabbii.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ↔ 𝜓)) |
| 3 | 2 | rabbiia 3440 | 1 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∈ 𝐴 ∣ 𝜓} |
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