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Theorem ertrd 6913
Description: A transitivity relation for equivalences. (Contributed by Mario Carneiro, 9-Jul-2014.)
Hypotheses
Ref Expression
ersymb.1
ertrd.5
ertrd.6
Assertion
Ref Expression
ertrd

Proof of Theorem ertrd
StepHypRef Expression
1 ertrd.5 . 2
2 ertrd.6 . 2
3 ersymb.1 . . 3
43ertr 6912 . 2
51, 2, 4mp2and 661 1
Colors of variables: wff set class
Syntax hints:  ->wi 4   class class class wbr 4204  Erwer 6894
This theorem is referenced by:  ertr2d  6914  ertr3d  6915  ertr4d  6916  erinxp  6970  nqereq  8804  adderpq  8825  mulerpq  8826  efgred2  15377  efgcpbllemb  15379  efgcpbl2  15381  pcophtb  19046  pi1xfr  19072  pi1xfrcnvlem  19073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-xp 4876  df-rel 4877  df-co 4879  df-er 6897
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