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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 1826 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓)) | |
2 | albii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
3 | 1, 2 | mpg 1805 | 1 ⊢ (∀𝑥𝜑 ↔ ∀𝑥𝜓) |
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