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| Mirrors > Home > MPE Home > Th. List > Mathboxes > exisym1 | Structured version Visualization version GIF version | ||
| Description: A symmetry with ∃. See negsym1 36418 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) | 
| Ref | Expression | 
|---|---|
| exisym1 | ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nfe1 2150 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
| 2 | falim 1557 | . . 3 ⊢ (⊥ → 𝜑) | |
| 3 | 2 | eximi 1835 | . 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑) | 
| 4 | 1, 3 | exlimi 2217 | 1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ⊥wfal 1552 ∃wex 1779 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-12 2177 | 
| This theorem depends on definitions: df-bi 207 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 | 
| This theorem is referenced by: (None) | 
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