Theorem prtlem80 39838

Description: Lemma for prter2 39858. (Contributed by Rodolfo Medina, 17-Oct-2010.)

Assertion

Ref	Expression
prtlem80	⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴}))

Proof of Theorem prtlem80

Step	Hyp	Ref	Expression
1		neldifsnd 4755	1 ⊢ (𝐴 ∈ 𝐵 → ¬ 𝐴 ∈ (𝐶 ∖ {𝐴}))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∈ wcel 2145   ∖ cdif 3895  {csn 4583

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-v 3452  df-dif 3901  df-sn 4584

This theorem is used by: (None)