Theorem unisym1 36389

Description: A symmetry with ∀.

See negsym1 36383 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 1554	. . 3 ⊢ (⊥ → ∀𝑥𝜑)
2	1	sps 2186	. 2 ⊢ (∀𝑥⊥ → ∀𝑥𝜑)
3	2	sps 2186	1 ⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1535  ⊥wfal 1549

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-tru 1540  df-fal 1550  df-ex 1778

This theorem is referenced by: (None)