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Theorem fvresval 25391
 Description: The value of a function at a restriction is either null or the same as the function itself. (Contributed by Scott Fenton, 4-Sep-2011.)
Assertion
Ref Expression
fvresval

Proof of Theorem fvresval
StepHypRef Expression
1 exmid 405 . 2
2 fvres 5745 . . 3
3 nfvres 5760 . . 3
42, 3orim12i 503 . 2
51, 4ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 358   wceq 1652   wcel 1725  c0 3628   cres 4880  cfv 5454 This theorem is referenced by:  sltres  25619 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-xp 4884  df-dm 4888  df-res 4890  df-iota 5418  df-fv 5462
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