Theorem qlax2i 29186

Description: One of the equations showing C_ℋ is an ortholattice. (This corresponds to axiom "ax-2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)

Hypotheses

Ref	Expression
qlax.1	⊢ 𝐴 ∈ Cℋ
qlax.2	⊢ 𝐵 ∈ Cℋ

Assertion

Ref	Expression
qlax2i	⊢ (𝐴 ∨ℋ 𝐵) = (𝐵 ∨ℋ 𝐴)

Proof of Theorem qlax2i

Step	Hyp	Ref	Expression
1		qlax.1	. 2 ⊢ 𝐴 ∈ Cℋ
2		qlax.2	. 2 ⊢ 𝐵 ∈ Cℋ
3	1, 2	chjcomi 29026	1 ⊢ (𝐴 ∨ℋ 𝐵) = (𝐵 ∨ℋ 𝐴)

Syntax hints:   = wceq 1507   ∈ wcel 2050  (class class class)co 6976   C_ℋ cch 28485   ∨_ℋ chj 28489

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2750  ax-sep 5060  ax-nul 5067  ax-pr 5186  ax-hilex 28555

This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2584  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ral 3093  df-rex 3094  df-rab 3097  df-v 3417  df-sbc 3682  df-dif 3832  df-un 3834  df-in 3836  df-ss 3843  df-nul 4179  df-if 4351  df-pw 4424  df-sn 4442  df-pr 4444  df-op 4448  df-uni 4713  df-br 4930  df-opab 4992  df-id 5312  df-xp 5413  df-rel 5414  df-cnv 5415  df-co 5416  df-dm 5417  df-rn 5418  df-res 5419  df-ima 5420  df-iota 6152  df-fun 6190  df-fv 6196  df-ov 6979  df-oprab 6980  df-mpo 6981  df-sh 28763  df-ch 28777  df-chj 28868

This theorem is referenced by: (None)