Theorem unisym1 36993

Description: A symmetry with ∀.

See negsym1 36987 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 1587	. . 3 ⊢ (⊥ → ∀𝑥𝜑)
2	1	sps 2224	. 2 ⊢ (∀𝑥⊥ → ∀𝑥𝜑)
3	2	sps 2224	1 ⊢ (∀𝑥∀𝑥⊥ → ∀𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-tru 1573  df-fal 1583  df-ex 1813

This theorem is used by: (None)