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Mirrors > Home > MPE Home > Th. List > Mathboxes > unisym1 | Structured version Visualization version GIF version |
Description: A symmetry with ∀.
See negsym1 33769 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) (Proof shortened by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
unisym1 | ⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | falim 1553 | . . 3 ⊢ (⊥ → ∀𝑥𝜑) | |
2 | 1 | sps 2183 | . 2 ⊢ (∀𝑥⊥ → ∀𝑥𝜑) |
3 | 2 | sps 2183 | 1 ⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 ⊥wfal 1548 |
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 1969 ax-7 2014 ax-12 2176 |
This theorem depends on definitions: df-bi 209 df-tru 1539 df-fal 1549 df-ex 1780 |
This theorem is referenced by: (None) |
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