Theorem qlaxr5i 29997

Description: One of the conditions showing C_ℋ is an ortholattice. (This corresponds to axiom "ax-r5" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)

Hypotheses

Ref	Expression
qlaxr5.1	⊢ 𝐴 ∈ Cℋ
qlaxr5.2	⊢ 𝐵 ∈ Cℋ
qlaxr5.3	⊢ 𝐶 ∈ Cℋ
qlaxr5.4	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
qlaxr5i	⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶)

Proof of Theorem qlaxr5i

Step	Hyp	Ref	Expression
1		qlaxr5.4	. 2 ⊢ 𝐴 = 𝐵
2	1	oveq1i 7285	1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶)

Syntax hints:   = wceq 1539   ∈ wcel 2106  (class class class)co 7275   C_ℋ cch 29291   ∨_ℋ chj 29295

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-iota 6391  df-fv 6441  df-ov 7278

This theorem is referenced by: (None)