Theorem qlaxr5i 31839

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 7407	1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶)

Syntax hints:   = wceq 1561   ∈ wcel 2143  (class class class)co 7397   C_ℋ cch 31133   ∨_ℋ chj 31137

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1564  df-fal 1574  df-ex 1801  df-sb 2092  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5102  df-iota 6478  df-fv 6530  df-ov 7400

This theorem is referenced by: (None)