Theorem qlaxr2i 29410

Description: One of the conditions showing C_ℋ is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)

Hypotheses

Ref	Expression
qlaxr2.1	⊢ 𝐴 ∈ Cℋ
qlaxr2.2	⊢ 𝐵 ∈ Cℋ
qlaxr2.3	⊢ 𝐶 ∈ Cℋ
qlaxr2.4	⊢ 𝐴 = 𝐵
qlaxr2.5	⊢ 𝐵 = 𝐶

Assertion

Ref	Expression
qlaxr2i	⊢ 𝐴 = 𝐶

Proof of Theorem qlaxr2i

Step	Hyp	Ref	Expression
1		qlaxr2.4	. 2 ⊢ 𝐴 = 𝐵
2		qlaxr2.5	. 2 ⊢ 𝐵 = 𝐶
3	1, 2	eqtri 2844	1 ⊢ 𝐴 = 𝐶

Syntax hints:   = wceq 1537   ∈ wcel 2114   C_ℋ cch 28706

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2124  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781  df-cleq 2814

This theorem is referenced by: (None)