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Theorem pm13.18 2588
Description: Theorem *13.18 in [WhiteheadRussell] p. 178. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.18 ((A = B AC) → BC)

Proof of Theorem pm13.18
StepHypRef Expression
1 eqeq1 2359 . . . 4 (A = B → (A = CB = C))
21biimprd 214 . . 3 (A = B → (B = CA = C))
32necon3d 2554 . 2 (A = B → (ACBC))
43imp 418 1 ((A = B AC) → BC)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   = wceq 1642  wne 2516
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-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-ne 2518
This theorem is referenced by:  pm13.181  2589
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