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Mirrors > Home > MPE Home > Th. List > 2eu2ex | Structured version Visualization version GIF version |
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2eu2ex | ⊢ (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2658 | . 2 ⊢ (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃!𝑦𝜑) | |
2 | euex 2658 | . . 3 ⊢ (∃!𝑦𝜑 → ∃𝑦𝜑) | |
3 | 2 | eximi 1831 | . 2 ⊢ (∃𝑥∃!𝑦𝜑 → ∃𝑥∃𝑦𝜑) |
4 | 1, 3 | syl 17 | 1 ⊢ (∃!𝑥∃!𝑦𝜑 → ∃𝑥∃𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1776 ∃!weu 2649 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-eu 2650 |
This theorem is referenced by: 2eu1 2731 2eu1OLD 2732 2eu1v 2733 |
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