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Theorem sseq12i 2965
Description: An equality inference for the subclass relationship. (Contributed by NM, 31-May-1999.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
sseq1i.1 A = B
sseq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
sseq12i (A𝐶B𝐷)

Proof of Theorem sseq12i
StepHypRef Expression
1 sseq1i.1 . 2 A = B
2 sseq12i.2 . 2 𝐶 = 𝐷
3 sseq12 2962 . 2 ((A = B 𝐶 = 𝐷) → (A𝐶B𝐷))
41, 2, 3mp2an 402 1 (A𝐶B𝐷)
Colors of variables: wff set class
Syntax hints:  wb 98   = 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:  3sstr3i  2977  3sstr4i  2978  3sstr3g  2979  3sstr4g  2980  ss2rab  3010
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