Theorem orfa2 38795

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

Hypothesis

Ref	Expression
orfa2.1	⊢ (𝜑 → ⊥)

Assertion

Ref	Expression
orfa2	⊢ ((𝜑 ∨ 𝜓) → 𝜓)

Proof of Theorem orfa2

Step	Hyp	Ref	Expression
1		orfa2.1	. . 3 ⊢ (𝜑 → ⊥)
2	1	orim1i 923	. 2 ⊢ ((𝜑 ∨ 𝜓) → (⊥ ∨ 𝜓))
3		falim 1587	. . 3 ⊢ (⊥ → 𝜓)
4		id 23	. . 3 ⊢ (𝜓 → 𝜓)
5	3, 4	jaoi 871	. 2 ⊢ ((⊥ ∨ 𝜓) → 𝜓)
6	2, 5	syl 18	1 ⊢ ((𝜑 ∨ 𝜓) → 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)