Theorem orfa1 38777

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 1587	. 2 ⊢ (⊥ → 𝜓)
3	1, 2	jaoi 871	1 ⊢ ((𝜑 ∨ ⊥) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∨ wo 861  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-tru 1573  df-fal 1583

This theorem is used by: (None)