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Metamath Proof Explorer
Description: Deduction form of Theorem 19.21 of Margaris p. 90. See 19.21 and
19.21v . (Contributed by NM, 10-Feb-1997)
|
|
Ref |
Expression |
|
Hypothesis |
alrimdv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
|
Assertion |
alrimdv |
⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
alrimdv.1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
| 2 |
|
ax-5 |
⊢ ( 𝜑 → ∀ 𝑥 𝜑 ) |
| 3 |
|
ax-5 |
⊢ ( 𝜓 → ∀ 𝑥 𝜓 ) |
| 4 |
2 3 1
|
alrimdh |
⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) ) |