Theorem cvnref 32899

Description: The covers relation is not reflexive. (Contributed by NM, 26-Jun-2004.) (New usage is discouraged.)

Assertion

Ref	Expression
cvnref	⊢ (𝐴 ∈ Cℋ → ¬ 𝐴 ⋖ℋ 𝐴)

Proof of Theorem cvnref

Step	Hyp	Ref	Expression
1		cvnsym 32898	. . 3 ⊢ ((𝐴 ∈ Cℋ ∧ 𝐴 ∈ Cℋ ) → (𝐴 ⋖ℋ 𝐴 → ¬ 𝐴 ⋖ℋ 𝐴))
2	1	anidms 577	. 2 ⊢ (𝐴 ∈ Cℋ → (𝐴 ⋖ℋ 𝐴 → ¬ 𝐴 ⋖ℋ 𝐴))
3	2	pm2.01d 192	1 ⊢ (𝐴 ∈ Cℋ → ¬ 𝐴 ⋖ℋ 𝐴)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∈ wcel 2144   class class class wbr 5102   C_ℋ cch 31537   ⋖_ℋ ccv 31572

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-sep 5248  ax-pr 5390

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-rex 3087  df-rab 3413  df-v 3452  df-ss 3896  df-pss 4014  df-dif 4047  df-in 4091  df-un 4151  df-nul 4279  df-if 4482  df-sn 4585  df-pr 4587  df-op 4835  df-br 5103  df-opab 5167  df-cv 32887

This theorem is used by: (None)