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Mirrors > Home > MPE Home > Th. List > 2eumo | Structured version Visualization version GIF version |
Description: Nested unique existential quantifier and at-most-one quantifier. (Contributed by NM, 3-Dec-2001.) |
Ref | Expression |
---|---|
2eumo | ⊢ (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euimmo 2617 | . 2 ⊢ (∀𝑥(∃!𝑦𝜑 → ∃*𝑦𝜑) → (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)) | |
2 | eumo 2577 | . 2 ⊢ (∃!𝑦𝜑 → ∃*𝑦𝜑) | |
3 | 1, 2 | mpg 1805 | 1 ⊢ (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃*wmo 2537 ∃!weu 2567 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 df-mo 2539 df-eu 2568 |
This theorem is referenced by: (None) |
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