Theorem dissym1

Description: A symmetry with \/ .

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

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

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜓 → ( 𝜓 ∨ 𝜑 ) )
2		falim	⊢ ( ⊥ → 𝜑 )
3	2	orim2i	⊢ ( ( 𝜓 ∨ ⊥ ) → ( 𝜓 ∨ 𝜑 ) )
4	1 3	jaoi	⊢ ( ( 𝜓 ∨ ( 𝜓 ∨ ⊥ ) ) → ( 𝜓 ∨ 𝜑 ) )