Theorem idorfalsel-P4.20a 440

Description: '∨' Identity is '⊥' (left). †

Assertion

Ref	Expression
idorfalsel-P4.20a	⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)

Proof of Theorem idorfalsel-P4.20a

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . . 4 ⊢ (((⊥ ∨ 𝜑) ∧ ⊥) → ⊥)
2	1	falseimpoe-P4.4c 383	. . 3 ⊢ (((⊥ ∨ 𝜑) ∧ ⊥) → 𝜑)
3		rcp-NDASM2of2 194	. . 3 ⊢ (((⊥ ∨ 𝜑) ∧ 𝜑) → 𝜑)
4		rcp-NDASM1of1 192	. . 3 ⊢ ((⊥ ∨ 𝜑) → (⊥ ∨ 𝜑))
5	2, 3, 4	rcp-NDORE2 235	. 2 ⊢ ((⊥ ∨ 𝜑) → 𝜑)
6		ndoril-P3.10.CL 245	. 2 ⊢ (𝜑 → (⊥ ∨ 𝜑))
7	5, 6	rcp-NDBII0 239	1 ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wff-bi 104   ∧ wff-and 132   ∨ wff-or 144  ⊥wff-false 157

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  df-false-D2.5 158

This theorem is referenced by:  idorfalser-P4.20b  441  idornthml-P4.24a  448  truthtblfort-P4.38c  505  truthtblforf-P4.38d  506