Mathbox for Anthony Hart |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > exisym1 | Structured version Visualization version GIF version |
Description: A symmetry with ∃.
See negsym1 34244 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) |
Ref | Expression |
---|---|
exisym1 | ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2155 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | falim 1559 | . . 3 ⊢ (⊥ → 𝜑) | |
3 | 2 | eximi 1841 | . 2 ⊢ (∃𝑥⊥ → ∃𝑥𝜑) |
4 | 1, 3 | exlimi 2219 | 1 ⊢ (∃𝑥∃𝑥⊥ → ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥wfal 1554 ∃wex 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-10 2145 ax-12 2179 |
This theorem depends on definitions: df-bi 210 df-tru 1545 df-fal 1555 df-ex 1787 df-nf 1791 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |