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Theorem 3sstr3g 3311
 Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 1-Oct-2000.)
Hypotheses
Ref Expression
3sstr3g.1 (φA B)
3sstr3g.2 A = C
3sstr3g.3 B = D
Assertion
Ref Expression
3sstr3g (φC D)

Proof of Theorem 3sstr3g
StepHypRef Expression
1 3sstr3g.1 . 2 (φA B)
2 3sstr3g.2 . . 3 A = C
3 3sstr3g.3 . . 3 B = D
42, 3sseq12i 3297 . 2 (A BC D)
51, 4sylib 188 1 (φC D)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ⊆ wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 This theorem is referenced by:  uniintsn  3963  cnvtr  5098
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