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Theorem mpoeq3dva 5801
 Description: Slightly more general equality inference for the maps-to notation. (Contributed by NM, 17-Oct-2013.)
Hypothesis
Ref Expression
mpoeq3dva.1
Assertion
Ref Expression
mpoeq3dva
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem mpoeq3dva
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpoeq3dva.1 . . . . . 6
213expb 1165 . . . . 5
32eqeq2d 2127 . . . 4
43pm5.32da 445 . . 3
54oprabbidv 5791 . 2
6 df-mpo 5745 . 2
7 df-mpo 5745 . 2
85, 6, 73eqtr4g 2173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 945   wceq 1314   wcel 1463  coprab 5741   cmpo 5742 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-oprab 5744  df-mpo 5745 This theorem is referenced by:  mpoeq3ia  5802  mpoeq3dv  5803  ofeq  5950  fmpoco  6079  mapxpen  6708  seqeq2  10173  seqeq3  10174  cnmpt2t  12368  cnmpt22  12369  cnmptcom  12373
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