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Theorem mpteq12i 5665
 Description: An equality inference for the maps to notation. (Contributed by Scott Fenton, 27-Oct-2010.)
Hypotheses
Ref Expression
mpteq12i.1 A = C
mpteq12i.2 B = D
Assertion
Ref Expression
mpteq12i (x A B) = (x C D)

Proof of Theorem mpteq12i
StepHypRef Expression
1 mpteq12i.1 . . . 4 A = C
21a1i 10 . . 3 ( ⊤ → A = C)
3 mpteq12i.2 . . . 4 B = D
43a1i 10 . . 3 ( ⊤ → B = D)
52, 4mpteq12dv 5656 . 2 ( ⊤ → (x A B) = (x C D))
65trud 1323 1 (x A B) = (x C D)
 Colors of variables: wff setvar class Syntax hints:   ⊤ wtru 1316   = wceq 1642   ↦ cmpt 5651 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-ral 2619  df-opab 4623  df-mpt 5652 This theorem is referenced by: (None)
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