qlaxr1i - Hilbert Space Explorer

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Theorem qlaxr1i 29403

Description: One of the conditions showing C_ℋ is an ortholattice. (This corresponds to axiom "ax-r1" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)

**Hypotheses**
Ref	Expression
qlaxr1.1	⊢ 𝐴 ∈ C_ℋ
qlaxr1.2	⊢ 𝐵 ∈ C_ℋ
qlaxr1.3	⊢ 𝐴 = 𝐵

**Assertion**
Ref	Expression
qlaxr1i	⊢ 𝐵 = 𝐴

**Proof of Theorem qlaxr1i**
Step	Hyp	Ref	Expression
1		qlaxr1.3	. 2 ⊢ 𝐴 = 𝐵
2	1	eqcomi 2830	1 ⊢ 𝐵 = 𝐴

Colors of variables: wff setvar class

Syntax hints: = wceq 1533 ∈ wcel 2110 C_ℋ cch 28700

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-9 2120 ax-ext 2793

This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-cleq 2814

This theorem is referenced by: (None)

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