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Theorem breqtri 3787
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtr.1
breqtr.2
Assertion
Ref Expression
breqtri

Proof of Theorem breqtri
StepHypRef Expression
1 breqtr.1 . 2
2 breqtr.2 . . 3
32breq2i 3772 . 2
41, 3mpbi 133 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   class class class wbr 3764 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765 This theorem is referenced by:  breqtrri  3789  3brtr3i  3791  sqrt2gt1lt2  9647  ex-fl  9895
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