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Theorem eqsstrrdi 3208
Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
eqsstrrdi.1 (𝜑𝐵 = 𝐴)
eqsstrrdi.2 𝐵𝐶
Assertion
Ref Expression
eqsstrrdi (𝜑𝐴𝐶)

Proof of Theorem eqsstrrdi
StepHypRef Expression
1 eqsstrrdi.1 . . 3 (𝜑𝐵 = 𝐴)
21eqcomd 2183 . 2 (𝜑𝐴 = 𝐵)
3 eqsstrrdi.2 . 2 𝐵𝐶
42, 3eqsstrdi 3207 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  ffvresb  5679  tposss  6246  sbthlemi5  6959  iooval2  9913  telfsumo  11469  structcnvcnv  12472  ressbasssd  12523  txss12  13659  txbasval  13660
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