Theorem orfa1 35357

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

Hypothesis

Ref	Expression
orfa1.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
orfa1	⊢ ((𝜑 ∨ ⊥) → 𝜓)

Proof of Theorem orfa1

Step	Hyp	Ref	Expression
1		orfa1.1	. 2 ⊢ (𝜑 → 𝜓)
2		falim 1550	. 2 ⊢ (⊥ → 𝜓)
3	1, 2	jaoi 853	1 ⊢ ((𝜑 ∨ ⊥) → 𝜓)

Syntax hints:   → wi 4   ∨ wo 843  ⊥wfal 1545

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-or 844  df-tru 1536  df-fal 1546

This theorem is referenced by: (None)