Theorem orfa2

Description: Remove a contradicting disjunct from an antecedent. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Hypothesis	orfa2.1	⊢ ( 𝜑 → ⊥ )
Assertion	orfa2	⊢ ( ( 𝜑 ∨ 𝜓 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		orfa2.1	⊢ ( 𝜑 → ⊥ )
2	1	orim1i	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( ⊥ ∨ 𝜓 ) )
3		falim	⊢ ( ⊥ → 𝜓 )
4		id	⊢ ( 𝜓 → 𝜓 )
5	3 4	jaoi	⊢ ( ( ⊥ ∨ 𝜓 ) → 𝜓 )
6	2 5	syl	⊢ ( ( 𝜑 ∨ 𝜓 ) → 𝜓 )