Theorem qlaxr4i 31723

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 6830	1 ⊢ (⊥‘𝐴) = (⊥‘𝐵)

Syntax hints:   = wceq 1547   ∈ wcel 2119  ‘cfv 6485   C_ℋ cch 31018  ⊥cort 31019

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-ss 3900  df-nul 4262  df-if 4455  df-sn 4556  df-pr 4558  df-op 4562  df-uni 4839  df-br 5073  df-iota 6441  df-fv 6493

This theorem is referenced by: (None)