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Mirrors > Home > ILE Home > Th. List > euorv | GIF version |
Description: Introduce a disjunct into a unique existential quantifier. (Contributed by NM, 23-Mar-1995.) |
Ref | Expression |
---|---|
euorv | ⊢ ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1537 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | euor 2064 | 1 ⊢ ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑 ∨ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 104 ∨ wo 709 ∃!weu 2038 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-eu 2041 |
This theorem is referenced by: eueq2dc 2925 |
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