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Theorem pm13.18 2280
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 2043 . . . 4 (A = B → (A = 𝐶B = 𝐶))
21biimprd 147 . . 3 (A = B → (B = 𝐶A = 𝐶))
32necon3d 2243 . 2 (A = B → (A𝐶B𝐶))
43imp 115 1 ((A = B A𝐶) → B𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   = wceq 1242  wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by:  pm13.181  2281
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