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Mirrors > Home > MPE Home > Th. List > rgen | Structured version Visualization version GIF version |
Description: Generalization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.) |
Ref | Expression |
---|---|
rgen.1 | ⊢ (𝑥 ∈ 𝐴 → 𝜑) |
Ref | Expression |
---|---|
rgen | ⊢ ∀𝑥 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 3069 | . 2 ⊢ (∀𝑥 ∈ 𝐴 𝜑 ↔ ∀𝑥(𝑥 ∈ 𝐴 → 𝜑)) | |
2 | rgen.1 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝜑) | |
3 | 1, 2 | mpgbir 1802 | 1 ⊢ ∀𝑥 ∈ 𝐴 𝜑 |
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