Theorem unisym1 37335

Description: A symmetry with ∀.

See negsym1 37329 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 1586	. . 3 ⊢ (⊥ → ∀𝑥𝜑)
2	1	sps 2221	. 2 ⊢ (∀𝑥⊥ → ∀𝑥𝜑)
3	2	sps 2221	1 ⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

This proof depends on definitions:  df-bi 210  df-tru 1572  df-fal 1582  df-ex 1812

This theorem is used by: (None)