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Mirrors > Home > MPE Home > Th. List > Mathboxes > amosym1 | Structured version Visualization version GIF version |
Description: A symmetry with ∃*.
See negsym1 36400 for more information. (Contributed by Anthony Hart, 13-Sep-2011.) |
Ref | Expression |
---|---|
amosym1 | ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mofal 36392 | . . 3 ⊢ ∃*𝑥⊥ | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → ∃*𝑥⊥) |
3 | 2 | moimi 2543 | 1 ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊥wfal 1549 ∃*wmo 2536 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 |
This theorem depends on definitions: df-bi 207 df-or 848 df-tru 1540 df-fal 1550 df-ex 1777 df-mo 2538 |
This theorem is referenced by: (None) |
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