Theorem qlaxr4i 31986

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 6884	1 ⊢ (⊥‘𝐴) = (⊥‘𝐵)

Syntax hints:   = wceq 1570   ∈ wcel 2143  ‘cfv 6536   C_ℋ cch 31281  ⊥cort 31282

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-iota 6492  df-fv 6544

This theorem is referenced by: (None)