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Theorem 3sstr4i 3310
 Description: Substitution of equality in both sides of a subclass relationship. (Contributed by NM, 13-Jan-1996.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
3sstr4.1 A B
3sstr4.2 C = A
3sstr4.3 D = B
Assertion
Ref Expression
3sstr4i C D

Proof of Theorem 3sstr4i
StepHypRef Expression
1 3sstr4.1 . 2 A B
2 3sstr4.2 . . 3 C = A
3 3sstr4.3 . . 3 D = B
42, 3sseq12i 3297 . 2 (C DA B)
51, 4mpbir 200 1 C D
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ⊆ 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-ss 3259 This theorem is referenced by:  rncoss  4972  imassrn  5009  rnin  5037  ssoprab2i  5580
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