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| Mirrors > Home > MPE Home > Th. List > albii | Structured version Visualization version GIF version | ||
| Description: Inference adding universal quantifier to both sides of an equivalence. (Contributed by NM, 7-Aug-1994.) |
| Ref | Expression |
|---|---|
| albii.1 | ⊢ (𝜑 ↔ 𝜓) |
| Ref | Expression |
|---|---|
| albii | ⊢ (∀𝑥𝜑 ↔ ∀𝑥𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | albi 1818 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓)) | |
| 2 | albii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
| 3 | 1, 2 | mpg 1797 | 1 ⊢ (∀𝑥𝜑 ↔ ∀𝑥𝜓) |
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