Theorem bj-falor2 32570

Description: Dual of truan 1501. (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 1498	. . 3 ⊢ (⊥ → 𝜑)
2	1	bj-jaoi1 32556	. 2 ⊢ ((⊥ ∨ 𝜑) → 𝜑)
3		olc 399	. 2 ⊢ (𝜑 → (⊥ ∨ 𝜑))
4	2, 3	impbii 199	1 ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 196   ∨ wo 383  ⊥wfal 1488

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 197  df-or 385  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)