Theorem imsym1

Description: A symmetry with -> .

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

	Ref	Expression
Assertion	imsym1	⊢ ( ( 𝜓 → ( 𝜓 → ⊥ ) ) → ( 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ 𝜓 → ( 𝜓 → 𝜑 ) )
2		falim	⊢ ( ⊥ → 𝜑 )
3	2	imim2i	⊢ ( ( 𝜓 → ⊥ ) → ( 𝜓 → 𝜑 ) )
4	1 3	ja	⊢ ( ( 𝜓 → ( 𝜓 → ⊥ ) ) → ( 𝜓 → 𝜑 ) )