Theorem bj-falor2 34767

Description: Dual of truan 1550. (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 1556	. . 3 ⊢ (⊥ → 𝜑)
2	1	bj-jaoi1 34752	. 2 ⊢ ((⊥ ∨ 𝜑) → 𝜑)
3		olc 865	. 2 ⊢ (𝜑 → (⊥ ∨ 𝜑))
4	2, 3	impbii 208	1 ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 205   ∨ wo 844  ⊥wfal 1551

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 206  df-or 845  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)