Theorem qlaxr4i 30874

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 6891	1 ⊢ (⊥‘𝐴) = (⊥‘𝐵)

Syntax hints:   = wceq 1541   ∈ wcel 2106  ‘cfv 6540   C_ℋ cch 30169  ⊥cort 30170

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  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 6492  df-fv 6548

This theorem is referenced by: (None)