Description: Obsolete version of reximdvai as of 3-Nov-2024. (Contributed by NM, 14-Nov-2002) Reduce dependencies on axioms. (Revised by Wolf Lammen, 8-Jan-2020) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | reximdvai.1 | ⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → ( 𝜓 → 𝜒 ) ) ) | |
Assertion | reximdvaiOLD | ⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → ∃ 𝑥 ∈ 𝐴 𝜒 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reximdvai.1 | ⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → ( 𝜓 → 𝜒 ) ) ) | |
2 | 1 | ralrimiv | ⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 ( 𝜓 → 𝜒 ) ) |
3 | rexim | ⊢ ( ∀ 𝑥 ∈ 𝐴 ( 𝜓 → 𝜒 ) → ( ∃ 𝑥 ∈ 𝐴 𝜓 → ∃ 𝑥 ∈ 𝐴 𝜒 ) ) | |
4 | 2 3 | syl | ⊢ ( 𝜑 → ( ∃ 𝑥 ∈ 𝐴 𝜓 → ∃ 𝑥 ∈ 𝐴 𝜒 ) ) |