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Theorem eqsstr3d 2974
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
eqsstr3d.1 (φB = A)
eqsstr3d.2 (φB𝐶)
Assertion
Ref Expression
eqsstr3d (φA𝐶)

Proof of Theorem eqsstr3d
StepHypRef Expression
1 eqsstr3d.1 . . 3 (φB = A)
21eqcomd 2042 . 2 (φA = B)
3 eqsstr3d.2 . 2 (φB𝐶)
42, 3eqsstrd 2973 1 (φA𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = 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:  ssxpbm  4699  ssxp1  4700  ssxp2  4701  suppssof1  5670  tfrlemiubacc  5885  oaword1  5989  archnqq  6400
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