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Theorem mpt2eq123i 5750
 Description: An equality inference for the maps-to notation. (Contributed by NM, 15-Jul-2013.)
Hypotheses
Ref Expression
mpt2eq123i.1
mpt2eq123i.2
mpt2eq123i.3
Assertion
Ref Expression
mpt2eq123i

Proof of Theorem mpt2eq123i
StepHypRef Expression
1 mpt2eq123i.1 . . . 4
21a1i 9 . . 3
3 mpt2eq123i.2 . . . 4
43a1i 9 . . 3
5 mpt2eq123i.3 . . . 4
65a1i 9 . . 3
72, 4, 6mpt2eq123dv 5749 . 2
87mptru 1305 1
 Colors of variables: wff set class Syntax hints:   wceq 1296   wtru 1297   cmpt2 5692 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 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-11 1449  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-oprab 5694  df-mpt2 5695 This theorem is referenced by:  ofmres  5945
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