Theorem qlax2i 29866

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 29706	1 ⊢ (𝐴 ∨ℋ 𝐵) = (𝐵 ∨ℋ 𝐴)

Syntax hints:   = wceq 1543   ∈ wcel 2112  (class class class)co 7252   C_ℋ cch 29167   ∨_ℋ chj 29171

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2160  ax-12 2177  ax-ext 2710  ax-sep 5216  ax-nul 5223  ax-pr 5346  ax-hilex 29237

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-nf 1792  df-sb 2073  df-mo 2541  df-eu 2570  df-clab 2717  df-cleq 2731  df-clel 2818  df-nfc 2889  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3425  df-sbc 3713  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4255  df-if 4457  df-pw 4532  df-sn 4559  df-pr 4561  df-op 4565  df-uni 4837  df-br 5071  df-opab 5133  df-id 5479  df-xp 5585  df-rel 5586  df-cnv 5587  df-co 5588  df-dm 5589  df-rn 5590  df-res 5591  df-ima 5592  df-iota 6373  df-fun 6417  df-fv 6423  df-ov 7255  df-oprab 7256  df-mpo 7257  df-sh 29445  df-ch 29459  df-chj 29548

This theorem is referenced by: (None)