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Mirrors > Home > ILE Home > Th. List > euorv | GIF version |
Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 23-Mar-1995.) |
Ref | Expression |
---|---|
euorv | ⊢ ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1462 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | euor 1971 | 1 ⊢ ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑 ∨ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 102 ∨ wo 662 ∃!weu 1945 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1379 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-4 1443 ax-17 1462 ax-ial 1470 |
This theorem depends on definitions: df-bi 115 df-tru 1290 df-fal 1293 df-eu 1948 |
This theorem is referenced by: eueq2dc 2778 |
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