Theorem qlaxr5i 31615

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 7356	1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶)

Syntax hints:   = wceq 1541   ∈ wcel 2111  (class class class)co 7346   C_ℋ cch 30909   ∨_ℋ chj 30913

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-v 3438  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4281  df-if 4473  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4857  df-br 5090  df-iota 6437  df-fv 6489  df-ov 7349

This theorem is referenced by: (None)