Theorem qlaxr5i 31667

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 7458	1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶)

Syntax hints:   = wceq 1537   ∈ wcel 2108  (class class class)co 7448   C_ℋ cch 30961   ∨_ℋ chj 30965

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-iota 6525  df-fv 6581  df-ov 7451

This theorem is referenced by: (None)