Theorem pm2.61dan

Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005)

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

Proof

Step	Hyp	Ref	Expression
1		pm2.61dan.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		pm2.61dan.2	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜒 )
3	1	ex	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	2	ex	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
5	3 4	pm2.61d	⊢ ( 𝜑 → 𝜒 )