Theorem pm2.61ddan

Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013)

	Ref	Expression
Hypotheses	pm2.61ddan.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
	pm2.61ddan.2	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
	pm2.61ddan.3	⊢ ( ( 𝜑 ∧ ( ¬ 𝜓 ∧ ¬ 𝜒 ) ) → 𝜃 )
Assertion	pm2.61ddan	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		pm2.61ddan.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
2		pm2.61ddan.2	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
3		pm2.61ddan.3	⊢ ( ( 𝜑 ∧ ( ¬ 𝜓 ∧ ¬ 𝜒 ) ) → 𝜃 )
4	2	adantlr	⊢ ( ( ( 𝜑 ∧ ¬ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
5	3	anassrs	⊢ ( ( ( 𝜑 ∧ ¬ 𝜓 ) ∧ ¬ 𝜒 ) → 𝜃 )
6	4 5	pm2.61dan	⊢ ( ( 𝜑 ∧ ¬ 𝜓 ) → 𝜃 )
7	1 6	pm2.61dan	⊢ ( 𝜑 → 𝜃 )