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Theorem mpt2eq3dva 5729
 Description: Slightly more general equality inference for the maps-to notation. (Contributed by NM, 17-Oct-2013.)
Hypothesis
Ref Expression
mpt2eq3dva.1
Assertion
Ref Expression
mpt2eq3dva
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem mpt2eq3dva
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mpt2eq3dva.1 . . . . . 6
213expb 1145 . . . . 5
32eqeq2d 2100 . . . 4
43pm5.32da 441 . . 3
54oprabbidv 5719 . 2
6 df-mpt2 5673 . 2
7 df-mpt2 5673 . 2
85, 6, 73eqtr4g 2146 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   w3a 925   wceq 1290   wcel 1439  coprab 5669   cmpt2 5670 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-oprab 5672  df-mpt2 5673 This theorem is referenced by:  mpt2eq3ia  5730  ofeq  5874  fmpt2co  5997  mapxpen  6620  iseqeq2  9922  iseqeq3  9923  iseqval  9934
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