Theorem qlaxr2i 32247

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 2786	1 ⊢ 𝐴 = 𝐶

This proof depends on syntax axioms:   = wceq 1569   ∈ wcel 2146   C_ℋ cch 31543

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-9 2156  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-cleq 2755

This theorem is used by: (None)