Theorem difssd 3356

Description: A difference of two classes is contained in the minuend. Deduction form of difss 3355. (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 3355	. 2 |- ( A \ B ) C_ A
2	1	a1i 9	1 |- ( ph -> ( A \ B ) C_ A )

This proof depends on syntax axioms:   -> wi 4   \ cdif 3217   C_ wss 3220

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-dif 3222  df-in 3226  df-ss 3233

This theorem is used by:  ballotfilemdifcfi  13225  ballotfilemdifcfz  13227  bj-charfun  16833  bj-charfundc  16834  wexmiddiffi  17044