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Theorem mpt2eq123dva 6358
 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:   ,   ,

Proof of Theorem mpt2eq123dva
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2eq123dva.3 . . . . . 6
21eqeq2d 2471 . . . . 5
32pm5.32da 641 . . . 4
4 mpt2eq123dva.2 . . . . . . . 8
54eleq2d 2527 . . . . . . 7
65pm5.32da 641 . . . . . 6
7 mpt2eq123dv.1 . . . . . . . 8
87eleq2d 2527 . . . . . . 7
98anbi1d 704 . . . . . 6
106, 9bitrd 253 . . . . 5
1110anbi1d 704 . . . 4
123, 11bitrd 253 . . 3
1312oprabbidv 6351 . 2
14 df-mpt2 6301 . 2
15 df-mpt2 6301 . 2
1613, 14, 153eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  {coprab 6297  e.cmpt2 6298 This theorem is referenced by:  mpt2eq123dv  6359  natpropd  15345  fucpropd  15346  curfpropd  15502  hofpropd  15536  istrkgl  23855  eengv  24282  elntg  24287  rngcifuestrc  32805  funcrngcsetc  32806  funcrngcsetcALT  32807  funcringcsetc  32843 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-oprab 6300  df-mpt2 6301
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