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Theorem 3sstr4i 2984
 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
3sstr4.2
3sstr4.3
Assertion
Ref Expression
3sstr4i

Proof of Theorem 3sstr4i
StepHypRef Expression
1 3sstr4.1 . 2
2 3sstr4.2 . . 3
3 3sstr4.3 . . 3
42, 3sseq12i 2971 . 2
51, 4mpbir 134 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  undif2ss  3299  pwsnss  3574  iinuniss  3737  brab2a  4393  rncoss  4602  imassrn  4679  rnin  4733  inimass  4740  imadiflem  4978  imainlem  4980  ssoprab2i  5593  npsspw  6569  axresscn  6936
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