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Theorem ssdif2d 3405
 Description: If A is contained in B and C is contained in D, then (A ∖ D) is contained in (B ∖ C). Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ssdifd.1 (φA B)
ssdif2d.2 (φC D)
Assertion
Ref Expression
ssdif2d (φ → (A D) (B C))

Proof of Theorem ssdif2d
StepHypRef Expression
1 ssdif2d.2 . . 3 (φC D)
21sscond 3403 . 2 (φ → (A D) (A C))
3 ssdifd.1 . . 3 (φA B)
43ssdifd 3402 . 2 (φ → (A C) (B C))
52, 4sstrd 3282 1 (φ → (A D) (B C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∖ cdif 3206   ⊆ wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259 This theorem is referenced by: (None)
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