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Mirrors > Home > MPE Home > Th. List > Mathboxes > exisym1 | Structured version Visualization version GIF version |
Description: A symmetry with ∃.
See negsym1 34606 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) |
Ref | Expression |
---|---|
exisym1 | ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2147 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | falim 1556 | . . 3 ⊢ (⊥ → 𝜑) | |
3 | 2 | eximi 1837 | . 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑) |
4 | 1, 3 | exlimi 2210 | 1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥wfal 1551 ∃wex 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-10 2137 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-tru 1542 df-fal 1552 df-ex 1783 df-nf 1787 |
This theorem is referenced by: (None) |
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