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Theorem difssd 3317
Description: A difference of two classes is contained in the minuend. Deduction form of difss 3316. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difssd  |-  ( ph  ->  ( A  \  B
)  C_  A )

Proof of Theorem difssd
StepHypRef Expression
1 difss 3316 . 2  |-  ( A 
\  B )  C_  A
21a1i 10 1  |-  ( ph  ->  ( A  \  B
)  C_  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3162    C_ wss 3165
This theorem is referenced by:  mrieqvlemd  13547  mrieqv2d  13557  indsum  23621  areacirclem5  25032
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-in 3172  df-ss 3179
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