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Mirrors > Home > MPE Home > Th. List > rexlimdv | Structured version Visualization version GIF version |
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 14-Nov-2002.) (Proof shortened by Eric Schmidt, 22-Dec-2006.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 14-Jan-2020.) |
Ref | Expression |
---|---|
rexlimdv.1 | ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) |
Ref | Expression |
---|---|
rexlimdv | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexlimdv.1 | . . . 4 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) | |
2 | 1 | com3l 87 | . . 3 ⊢ (𝑥 ∈ 𝐴 → (𝜓 → (𝜑 → 𝜒))) |
3 | 2 | rexlimiv 3009 | . 2 ⊢ (∃𝑥 ∈ 𝐴 𝜓 → (𝜑 → 𝜒)) |
4 | 3 | com12 32 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
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