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Mirrors > Home > ILE Home > Th. List > ralbidv | GIF version |
Description: Formula-building rule for restricted universal quantifier (deduction form). (Contributed by NM, 20-Nov-1994.) |
Ref | Expression |
---|---|
ralbidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
ralbidv | ⊢ (𝜑 → (∀𝑥 ∈ 𝐴 𝜓 ↔ ∀𝑥 ∈ 𝐴 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | ralbidv.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | ralbid 2455 | 1 ⊢ (𝜑 → (∀𝑥 ∈ 𝐴 𝜓 ↔ ∀𝑥 ∈ 𝐴 𝜒)) |
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