Theorem simplim

Description: Simplification. Similar to Theorem *3.26 (Simp) of WhiteheadRussell p. 112. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 21-Jul-2012)

	Ref	Expression
Assertion	simplim	⊢ ( ¬ ( 𝜑 → 𝜓 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )
2	1	con1i	⊢ ( ¬ ( 𝜑 → 𝜓 ) → 𝜑 )