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Theorem resdmdfsn 5324
 Description: Restricting a function to a domain without one element of the domain of the function, and adding a pair of this element and the function value of the element results in the function itself. (Contributed by AV, 2-Dec-2018.)
Assertion
Ref Expression
resdmdfsn

Proof of Theorem resdmdfsn
StepHypRef Expression
1 resindm 5323 . 2
2 indif1 3741 . . . . 5
3 incom 3690 . . . . . . 7
4 inv1 3812 . . . . . . 7
53, 4eqtri 2486 . . . . . 6
65difeq1i 3617 . . . . 5
72, 6eqtri 2486 . . . 4
87a1i 11 . . 3
98reseq2d 5278 . 2
101, 9eqtr3d 2500 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395   cvv 3109  \cdif 3472  i^icin 3474  {csn 4029  domcdm 5004  |cres 5006  Rel`wrel 5009 This theorem is referenced by:  funresdfunsn  6113 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-dm 5014  df-res 5016
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