Theorem qlaxr5i 31706

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 7377	1 ⊢ (𝐴 ∨ℋ 𝐶) = (𝐵 ∨ℋ 𝐶)

Syntax hints:   = wceq 1542   ∈ wcel 2114  (class class class)co 7367   C_ℋ cch 31000   ∨_ℋ chj 31004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4851  df-br 5086  df-iota 6454  df-fv 6506  df-ov 7370

This theorem is referenced by: (None)