Theorem qlaxr2 5526

Description: One of the conditions showing C_ℋ is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.)

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
qlaxr2	⊢ A = C

Proof of Theorem qlaxr2

Step	Hyp	Ref	Expression
1		qlaxr2.4	. 2 ⊢ A = B
2		qlaxr2.5	. 2 ⊢ B = C
3	1, 2	eqtr 1119	1 ⊢ A = C

Syntax hints:   = wceq 1091   ∈ wcel 1092   C_ℋ cch 4968

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-cleq 1097

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