qlaxr1i - Hilbert Space Explorer

	Hilbert Space Explorer		< Previous Next > Nearby theorems
Mirrors > Home > HSE Home > Th. List > qlaxr1i		Structured version Visualization version GIF version

Theorem qlaxr1i 30885

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 2742	1 ⊢ 𝐵 = 𝐴

Colors of variables: wff setvar class

Syntax hints: = wceq 1542 ∈ wcel 2107 C_ℋ cch 30182

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-9 2117 ax-ext 2704

This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 df-cleq 2725

This theorem is referenced by: (None)

W3C validator