Theorem orfa1

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

	Ref	Expression
Hypothesis	orfa1.1	⊢ ( 𝜑 → 𝜓 )
Assertion	orfa1	⊢ ( ( 𝜑 ∨ ⊥ ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		orfa1.1	⊢ ( 𝜑 → 𝜓 )
2		falim	⊢ ( ⊥ → 𝜓 )
3	1 2	jaoi	⊢ ( ( 𝜑 ∨ ⊥ ) → 𝜓 )