Theorem qlaxr4i 31154

Description: One of the conditions showing C_ℋ is an ortholattice. (This corresponds to axiom "ax-r4" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)

Hypotheses

Ref	Expression
qlaxr4.1	⊢ 𝐴 ∈ Cℋ
qlaxr4.2	⊢ 𝐵 ∈ Cℋ
qlaxr4.3	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
qlaxr4i	⊢ (⊥‘𝐴) = (⊥‘𝐵)

Proof of Theorem qlaxr4i

Step	Hyp	Ref	Expression
1		qlaxr4.3	. 2 ⊢ 𝐴 = 𝐵
2	1	fveq2i 6893	1 ⊢ (⊥‘𝐴) = (⊥‘𝐵)

Syntax hints:   = wceq 1539   ∈ wcel 2104  ‘cfv 6542   C_ℋ cch 30449  ⊥cort 30450

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-rab 3431  df-v 3474  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4322  df-if 4528  df-sn 4628  df-pr 4630  df-op 4634  df-uni 4908  df-br 5148  df-iota 6494  df-fv 6550

This theorem is referenced by: (None)