Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998) Reduce dependencies on axioms. (Revised by Wolf Lammen, 28-Dec-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ralrimdv.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝑥 ∈ 𝐴 → 𝜒 ) ) ) | |
| Assertion | ralrimdv | ⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 ∈ 𝐴 𝜒 ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralrimdv.1 | ⊢ ( 𝜑 → ( 𝜓 → ( 𝑥 ∈ 𝐴 → 𝜒 ) ) ) | |
| 2 | 1 | imp | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝑥 ∈ 𝐴 → 𝜒 ) ) |
| 3 | 2 | ralrimiv | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ∀ 𝑥 ∈ 𝐴 𝜒 ) |
| 4 | 3 | ex | ⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 ∈ 𝐴 𝜒 ) ) |