Theorem eldifi 1591

Description: Implication of membership in a class difference.

Assertion

Ref	Expression
eldifi	⊢ (A ∈ (B ∖ C) → A ∈ B)

Proof of Theorem eldifi

Step	Hyp	Ref	Expression
1		eldif 1496	. 2 ⊢ (A ∈ (B ∖ C) ↔ (A ∈ B ∧ ¬ A ∈ C))
2	1	pm3.26bd 259	1 ⊢ (A ∈ (B ∖ C) → A ∈ B)

Syntax hints:  ¬ wn 1   → wi 2   ∈ wcel 1092   ∖ cdif 1484

This theorem is referenced by:  difss 1596  tz7.7 2224  tfi 2244  peano5 2394  tz7.48-1 2994  tz7.49 2997  pssnn 3428  unblem1 3431  inf3lem3 3466  strlem1 5691  strlem3 5694  strlem4 5695  strlem5 5696

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489

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