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Theorem coeq2 4875
 Description: Equality theorem for composition of two classes. (Contributed by set.mm contributors, 3-Jan-1997.)
Assertion
Ref Expression
coeq2

Proof of Theorem coeq2
StepHypRef Expression
1 coss2 4873 . . 3
2 coss2 4873 . . 3
31, 2anim12i 549 . 2
4 eqss 3287 . 2
5 eqss 3287 . 2
63, 4, 53imtr4i 257 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wss 3257   ccom 4721 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623  df-br 4640  df-co 4726 This theorem is referenced by:  coeq2i  4877  coeq2d  4879  txpeq1  5779  txpeq2  5780  composevalg  5817  enmap1lem3  6071  enmap1lem5  6073
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