qlaxr1i - Hilbert Space Explorer

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Theorem qlaxr1i 31651

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 2746	1 ⊢ 𝐵 = 𝐴

Colors of variables: wff setvar class

Syntax hints: = wceq 1540 ∈ wcel 2108 C_ℋ cch 30948

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-9 2118 ax-ext 2708

This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-cleq 2729

This theorem is referenced by: (None)

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