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| Mirrors > Home > MPE Home > Th. List > Mathboxes > amosym1 | Structured version Visualization version GIF version | ||
| Description: A symmetry with ∃*. See negsym1 36418 for more information. (Contributed by Anthony Hart, 13-Sep-2011.) | 
| Ref | Expression | 
|---|---|
| amosym1 | ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | mofal 36410 | . . 3 ⊢ ∃*𝑥⊥ | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → ∃*𝑥⊥) | 
| 3 | 2 | moimi 2545 | 1 ⊢ (∃*𝑥∃*𝑥⊥ → ∃*𝑥𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ⊥wfal 1552 ∃*wmo 2538 | 
| 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 | 
| This theorem depends on definitions: df-bi 207 df-or 849 df-tru 1543 df-fal 1553 df-ex 1780 df-mo 2540 | 
| This theorem is referenced by: (None) | 
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