Theorem difssd 3286

Description: A difference of two classes is contained in the minuend. Deduction form of difss 3285. (Contributed by David Moews, 1-May-2017.)

Assertion

Ref	Expression
difssd	|- ( ph -> ( A \ B ) C_ A )

Proof of Theorem difssd

Step	Hyp	Ref	Expression
1		difss 3285	. 2 |- ( A \ B ) C_ A
2	1	a1i 9	1 |- ( ph -> ( A \ B ) C_ A )

Syntax hints:   -> wi 4   \ cdif 3150   C_ wss 3153

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 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-dif 3155  df-in 3159  df-ss 3166

This theorem is referenced by:  bj-charfun  15244  bj-charfundc  15245