Theorem pm2.61d

Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994) (Proof shortened by Wolf Lammen, 12-Sep-2013)

	Ref	Expression
Hypotheses	pm2.61d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	pm2.61d.2	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
Assertion	pm2.61d	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		pm2.61d.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		pm2.61d.2	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
3	2	con1d	⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜓 ) )
4	3 1	syld	⊢ ( 𝜑 → ( ¬ 𝜒 → 𝜒 ) )
5	4	pm2.18d	⊢ ( 𝜑 → 𝜒 )