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Theorem ssres 4990
 Description: Subclass theorem for restriction. (Contributed by set.mm contributors, 16-Aug-1994.)
Assertion
Ref Expression
ssres (A B → (A C) (B C))

Proof of Theorem ssres
StepHypRef Expression
1 ssrin 3480 . 2 (A B → (A ∩ (C × V)) (B ∩ (C × V)))
2 df-res 4788 . 2 (A C) = (A ∩ (C × V))
3 df-res 4788 . 2 (B C) = (B ∩ (C × V))
41, 2, 33sstr4g 3312 1 (A B → (A C) (B C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Vcvv 2859   ∩ cin 3208   ⊆ wss 3257   × cxp 4770   ↾ cres 4774 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-ss 3259  df-res 4788 This theorem is referenced by:  imass1  5023
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