MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  difssd Unicode version

Theorem difssd 3306
Description: A difference of two classes is contained in the minuend. Deduction form of difss 3305. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difssd  |-  ( ph  ->  ( A  \  B
)  C_  A )

Proof of Theorem difssd
StepHypRef Expression
1 difss 3305 . 2  |-  ( A 
\  B )  C_  A
21a1i 10 1  |-  ( ph  ->  ( A  \  B
)  C_  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \ cdif 3151    C_ wss 3154
This theorem is referenced by:  mrieqvlemd  13533  mrieqv2d  13543  indsum  23608  areacirclem5  24940
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-v 2792  df-dif 3157  df-in 3161  df-ss 3168
  Copyright terms: Public domain W3C validator