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Theorem ertrd 6970
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 6969 . 2
51, 2, 4mp2and 662 1
Colors of variables: wff set class
Syntax hints:  ->wi 4   class class class wbr 4243  Erwer 6951
This theorem is referenced by:  ertr2d  6971  ertr3d  6972  ertr4d  6973  erinxp  7027  nqereq  8863  adderpq  8884  mulerpq  8885  efgred2  15436  efgcpbllemb  15438  efgcpbl2  15440  pcophtb  19105  pi1xfr  19131  pi1xfrcnvlem  19132
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-sep 4364  ax-nul 4372  ax-pr 4442
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-ral 2717  df-rex 2718  df-rab 2721  df-v 2967  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3766  df-sn 3847  df-pr 3848  df-op 3850  df-br 4244  df-opab 4302  df-xp 4925  df-rel 4926  df-co 4928  df-er 6954
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