Theorem bj-falor2 37211

Description: Dual of truan 1581. (Contributed by BJ, 26-Oct-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-falor2	⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)

Proof of Theorem bj-falor2

Step	Hyp	Ref	Expression
1		falim 1587	. . 3 ⊢ (⊥ → 𝜑)
2	1	bj-jaoi1 37197	. 2 ⊢ ((⊥ ∨ 𝜑) → 𝜑)
3		olc 882	. 2 ⊢ (𝜑 → (⊥ ∨ 𝜑))
4	2, 3	impbii 212	1 ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)

This proof depends on syntax axioms:   ↔ wb 209   ∨ 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)