Theorem idempotor-P4.25b 451

Description: Idempotency Law for '∨'. †

Assertion

Ref	Expression
idempotor-P4.25b	⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Proof of Theorem idempotor-P4.25b

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ (((𝜑 ∨ 𝜑) ∧ 𝜑) → 𝜑)
2		rcp-NDASM1of1 192	. . 3 ⊢ ((𝜑 ∨ 𝜑) → (𝜑 ∨ 𝜑))
3	1, 1, 2	rcp-NDORE2 235	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
4		ndoril-P3.10.CL 245	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
5	3, 4	rcp-NDBII0 239	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wff-bi 104   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155

This theorem is referenced by:  oroverim-P4.28-L1  465  rimoverand-P4.31-L1  480  rimoveror-P4.31b  482  truthtbltort-P4.38a  503  joinimandinc3-P4  578  joinimor2-P4  584