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Mirrors > Home > MPE Home > Th. List > Mathboxes > exisym1 | Structured version Visualization version GIF version |
Description: A symmetry with ∃.
See negsym1 33767 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) |
Ref | Expression |
---|---|
exisym1 | ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2154 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | falim 1554 | . . 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 1549 ∃wex 1780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-tru 1540 df-fal 1550 df-ex 1781 df-nf 1785 |
This theorem is referenced by: (None) |
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