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Mirrors > Home > MPE Home > Th. List > vtoclg | Structured version Visualization version GIF version |
Description: Implicit substitution of a class expression for a setvar variable. (Contributed by NM, 17-Apr-1995.) |
Ref | Expression |
---|---|
vtoclg.1 | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
vtoclg.2 | ⊢ 𝜑 |
Ref | Expression |
---|---|
vtoclg | ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1873 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | vtoclg.1 | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
3 | vtoclg.2 | . 2 ⊢ 𝜑 | |
4 | 1, 2, 3 | vtoclg1f 3485 | 1 ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
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