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Theorem 3sstr4i 2978
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 AB
3sstr4.2 𝐶 = A
3sstr4.3 𝐷 = B
Assertion
Ref Expression
3sstr4i 𝐶𝐷

Proof of Theorem 3sstr4i
StepHypRef Expression
1 3sstr4.1 . 2 AB
2 3sstr4.2 . . 3 𝐶 = A
3 3sstr4.3 . . 3 𝐷 = B
42, 3sseq12i 2965 . 2 (𝐶𝐷AB)
51, 4mpbir 134 1 𝐶𝐷
Colors of variables: wff set class
Syntax hints:   = wceq 1242  wss 2911
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  undif2ss  3293  pwsnss  3565  iinuniss  3728  brab2a  4336  rncoss  4545  imassrn  4622  rnin  4676  inimass  4683  imadiflem  4921  imainlem  4923  ssoprab2i  5535  npsspw  6453  axresscn  6706
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