Theorem unisym1 36736

Description: A symmetry with ∀.

See negsym1 36730 for more information. (Contributed by Anthony Hart, 4-Sep-2011.) (Proof shortened by Mario Carneiro, 11-Dec-2016.)

Assertion

Ref	Expression
unisym1	⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑)

Proof of Theorem unisym1

Step	Hyp	Ref	Expression
1		falim 1576	. . 3 ⊢ (⊥ → ∀𝑥𝜑)
2	1	sps 2219	. 2 ⊢ (∀𝑥⊥ → ∀𝑥𝜑)
3	2	sps 2219	1 ⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1557  ⊥wfal 1571

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-tru 1562  df-fal 1572  df-ex 1799

This theorem is referenced by: (None)