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Theorem sseqtrd 2975
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtrd.1  C_
sseqtrd.2  C
Assertion
Ref Expression
sseqtrd  C_  C

Proof of Theorem sseqtrd
StepHypRef Expression
1 sseqtrd.1 . 2  C_
2 sseqtrd.2 . . 3  C
32sseq2d 2967 . 2  C_  C_  C
41, 3mpbid 135 1  C_  C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242    C_ 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:  sseqtr4d  2976  resasplitss  5012  nnaword2  6023  erssxp  6065  ioodisj  8631
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