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Theorem xpssres 4591
Description: Restriction of a constant function (or other cross product). (Contributed by Stefan O'Rear, 24-Jan-2015.)
Assertion
Ref Expression
xpssres  C 
C_  X.  |`  C  C  X.

Proof of Theorem xpssres
StepHypRef Expression
1 df-res 4303 . . 3  X.  |`  C  X.  i^i  C  X.  _V
2 inxp 4416 . . 3  X.  i^i  C  X.  _V  i^i  C  X.  i^i  _V
3 incom 3126 . . . 4  i^i  C  C  i^i
4 inv1 3250 . . . 4  i^i  _V
53, 4xpeq12i 4313 . . 3  i^i  C  X.  i^i  _V  C  i^i  X.
61, 2, 53eqtri 2064 . 2  X.  |`  C  C  i^i  X.
7 df-ss 2928 . . . 4  C 
C_  C  i^i  C
87biimpi 113 . . 3  C 
C_  C  i^i  C
98xpeq1d 4314 . 2  C 
C_  C  i^i  X.  C  X.
106, 9syl5eq 2084 1  C 
C_  X.  |`  C  C  X.
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1243   _Vcvv 2554    i^i cin 2913    C_ wss 2914    X. cxp 4289    |` cres 4293
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3869  ax-pow 3921  ax-pr 3938
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2308  df-rex 2309  df-v 2556  df-un 2919  df-in 2921  df-ss 2928  df-pw 3356  df-sn 3376  df-pr 3377  df-op 3379  df-opab 3813  df-xp 4297  df-rel 4298  df-res 4303
This theorem is referenced by: (None)
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