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Theorem mpt2eq123dva 5594
 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 2067 . . . . 5
32pm5.32da 433 . . . 4
4 mpt2eq123dva.2 . . . . . . . 8
54eleq2d 2123 . . . . . . 7
65pm5.32da 433 . . . . . 6
7 mpt2eq123dv.1 . . . . . . . 8
87eleq2d 2123 . . . . . . 7
98anbi1d 446 . . . . . 6
106, 9bitrd 181 . . . . 5
1110anbi1d 446 . . . 4
123, 11bitrd 181 . . 3
1312oprabbidv 5587 . 2
14 df-mpt2 5545 . 2
15 df-mpt2 5545 . 2
1613, 14, 153eqtr4g 2113 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wceq 1259   wcel 1409  coprab 5541   cmpt2 5542 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-oprab 5544  df-mpt2 5545 This theorem is referenced by:  mpt2eq123dv  5595
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