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Theorem mpt2eq123dv 5663
 Description: An equality deduction for the maps to notation. (Contributed by set.mm contributors, 12-Sep-2011.)
Hypotheses
Ref Expression
mpt2eq123dv.1
mpt2eq123dv.2
mpt2eq123dv.3
Assertion
Ref Expression
mpt2eq123dv
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)   (,)

Proof of Theorem mpt2eq123dv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2eq123dv.1 . . . . . 6
21eleq2d 2420 . . . . 5
3 mpt2eq123dv.2 . . . . . 6
43eleq2d 2420 . . . . 5
52, 4anbi12d 691 . . . 4
6 mpt2eq123dv.3 . . . . 5
76eqeq2d 2364 . . . 4
85, 7anbi12d 691 . . 3
98oprabbidv 5564 . 2
10 df-mpt2 5654 . 2
11 df-mpt2 5654 . 2
129, 10, 113eqtr4g 2410 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wceq 1642   wcel 1710  coprab 5527   cmpt2 5653 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-oprab 5528  df-mpt2 5654 This theorem is referenced by:  mpt2eq123i  5664
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