Theorem idorfalser-P4.20b 441

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

Assertion

Ref	Expression
idorfalser-P4.20b	⊢ ((𝜑 ∨ ⊥) ↔ 𝜑)

Proof of Theorem idorfalser-P4.20b

Step	Hyp	Ref	Expression
1		idorfalsel-P4.20a 440	. 2 ⊢ ((⊥ ∨ 𝜑) ↔ 𝜑)
2		orcomm-P3.37 319	. . . 4 ⊢ ((⊥ ∨ 𝜑) ↔ (𝜑 ∨ ⊥))
3	2	subbil-P3.41a.RC 333	. . 3 ⊢ (((⊥ ∨ 𝜑) ↔ 𝜑) ↔ ((𝜑 ∨ ⊥) ↔ 𝜑))
4	3	rcp-NDBIEF0 240	. 2 ⊢ (((⊥ ∨ 𝜑) ↔ 𝜑) → ((𝜑 ∨ ⊥) ↔ 𝜑))
5	1, 4	rcp-NDIME0 228	1 ⊢ ((𝜑 ∨ ⊥) ↔ 𝜑)

Syntax hints:   ↔ wff-bi 104   ∨ 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:  idornthmr-P4.24b  449  truthtbltorf-P4.38b  504