Theorem difss2d 3338

Description: If a class is contained in a difference, it is contained in the minuend. Deduction form of difss2 3337. (Contributed by David Moews, 1-May-2017.)

Hypothesis

Ref	Expression
difss2d.1	|- ( ph -> A C_ ( B \ C ) )

Assertion

Ref	Expression
difss2d	|- ( ph -> A C_ B )

Proof of Theorem difss2d

Step	Hyp	Ref	Expression
1		difss2d.1	. 2 |- ( ph -> A C_ ( B \ C ) )
2		difss2 3337	. 2 |- ( A C_ ( B \ C ) -> A C_ B )
3	1, 2	syl 14	1 |- ( ph -> A C_ B )

Syntax hints:   -> wi 4   \ cdif 3198   C_ wss 3201

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 619  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-dif 3203  df-in 3207  df-ss 3214

This theorem is referenced by: (None)