Theorem dissym1 34610

Description: A symmetry with ∨.

See negsym1 34606 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion

Ref	Expression
dissym1	⊢ ((𝜓 ∨ (𝜓 ∨ ⊥)) → (𝜓 ∨ 𝜑))

Proof of Theorem dissym1

Step	Hyp	Ref	Expression
1		orc 864	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑))
2		falim 1556	. . 3 ⊢ (⊥ → 𝜑)
3	2	orim2i 908	. 2 ⊢ ((𝜓 ∨ ⊥) → (𝜓 ∨ 𝜑))
4	1, 3	jaoi 854	1 ⊢ ((𝜓 ∨ (𝜓 ∨ ⊥)) → (𝜓 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ wo 844  ⊥wfal 1551

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 845  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)