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Theorem unisym1 32728
Description: A symmetry with .

See negsym1 32722 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) (Proof shortened by Mario Carneiro, 11-Dec-2016.)

Assertion
Ref Expression
unisym1 (∀𝑥𝑥⊥ → ∀𝑥𝜑)

Proof of Theorem unisym1
StepHypRef Expression
1 falim 1647 . . 3 (⊥ → ∀𝑥𝜑)
21sps 2202 . 2 (∀𝑥⊥ → ∀𝑥𝜑)
32sps 2202 1 (∀𝑥𝑥⊥ → ∀𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630  wfal 1637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-tru 1635  df-fal 1638  df-ex 1854
This theorem is referenced by: (None)
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