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Theorem mpt2eq123dva 6341
 Description: An equality deduction for the maps to notation. (Contributed by Mario Carneiro, 26-Jan-2017.)
Hypotheses
Ref Expression
mpt2eq123dv.1
mpt2eq123dva.2
mpt2eq123dva.3
Assertion
Ref Expression
mpt2eq123dva
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)   (,)

Proof of Theorem mpt2eq123dva
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2eq123dva.3 . . . . . 6
21eqeq2d 2418 . . . . 5
32pm5.32da 641 . . . 4
4 mpt2eq123dva.2 . . . . . . . 8
54eleq2d 2474 . . . . . . 7
65pm5.32da 641 . . . . . 6
7 mpt2eq123dv.1 . . . . . . . 8
87eleq2d 2474 . . . . . . 7
98anbi1d 705 . . . . . 6
106, 9bitrd 255 . . . . 5
1110anbi1d 705 . . . 4
123, 11bitrd 255 . . 3
1312oprabbidv 6334 . 2
14 df-mpt2 6285 . 2
15 df-mpt2 6285 . 2
1613, 14, 153eqtr4g 2470 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1407   wcel 1844  coprab 6281   cmpt2 6282 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-oprab 6284  df-mpt2 6285 This theorem is referenced by:  mpt2eq123dv  6342  natpropd  15591  fucpropd  15592  curfpropd  15828  hofpropd  15862  istrkgl  24236  eengv  24711  elntg  24716  rngcifuestrc  38329  funcrngcsetc  38330  funcrngcsetcALT  38331  funcringcsetc  38367
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