Theorem 3o1cs

Description: Deduction eliminating disjunct. (Contributed by Thierry Arnoux, 19-Dec-2016)

	Ref	Expression
Hypothesis	3o1cs.1	$$⊢\left(\phi \vee \psi \vee \chi \right)\to \theta$$
Assertion	3o1cs	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3o1cs.1	$$⊢\left(\phi \vee \psi \vee \chi \right)\to \theta$$
2		df-3or	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\left(\phi \vee \psi \right)\vee \chi \right)$$
3	2 1	sylbir	$$⊢\left(\left(\phi \vee \psi \right)\vee \chi \right)\to \theta$$
4	3	orcs	$$⊢\left(\phi \vee \psi \right)\to \theta$$
5	4	orcs	$$⊢\phi \to \theta$$