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Theorem smgrpisass 25158
 Description: A semi-group is associative. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.)
Assertion
Ref Expression
smgrpisass

Proof of Theorem smgrpisass
StepHypRef Expression
1 elin 3692 . . 3
21simprbi 464 . 2
3 df-sgrOLD 25156 . 2
42, 3eleq2s 2575 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1767   cin 3480  cass 25137  cmagm 25143  csem 25155 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-in 3488  df-sgrOLD 25156 This theorem is referenced by: (None)
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