Theorem qlaxr4i 31722

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 6845	1 ⊢ (⊥‘𝐴) = (⊥‘𝐵)

Syntax hints:   = wceq 1542   ∈ wcel 2114  ‘cfv 6500   C_ℋ cch 31017  ⊥cort 31018

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3402  df-v 3444  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4288  df-if 4482  df-sn 4583  df-pr 4585  df-op 4589  df-uni 4866  df-br 5101  df-iota 6456  df-fv 6508

This theorem is referenced by: (None)