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Theorem sseq1d 2966
Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994.)
Hypothesis
Ref Expression
sseq1d.1 (φA = B)
Assertion
Ref Expression
sseq1d (φ → (A𝐶B𝐶))

Proof of Theorem sseq1d
StepHypRef Expression
1 sseq1d.1 . 2 (φA = B)
2 sseq1 2960 . 2 (A = B → (A𝐶B𝐶))
31, 2syl 14 1 (φ → (A𝐶B𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  sseq12d  2968  eqsstrd  2973  snssg  3491  ssiun2s  3692  treq  3851  onsucsssucexmid  4212  funimass1  4919  feq1  4973  sbcfg  4988  fvmptssdm  5198  fvimacnvi  5224  nnsucsssuc  6010  ereq1  6049
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