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Metamath Proof Explorer
Description: Formula-building rule for universal quantifier (deduction form). See
also albidh and albid . (Contributed by NM, 26-May-1993)
|
|
Ref |
Expression |
|
Hypothesis |
albidv.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
Assertion |
albidv |
⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 ↔ ∀ 𝑥 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
albidv.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
| 2 |
|
ax-5 |
⊢ ( 𝜑 → ∀ 𝑥 𝜑 ) |
| 3 |
2 1
|
albidh |
⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 ↔ ∀ 𝑥 𝜒 ) ) |