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Theorem ofeq 6307
 Description: Equality theorem for function operation. (Contributed by Mario Carneiro, 20-Jul-2014.)
Assertion
Ref Expression
ofeq

Proof of Theorem ofeq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simp1 957 . . . . 5
21oveqd 6098 . . . 4
32mpteq2dv 4296 . . 3
43mpt2eq3dva 6138 . 2
5 df-of 6305 . 2
6 df-of 6305 . 2
74, 5, 63eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 936   wceq 1652   wcel 1725  cvv 2956   cin 3319   cmpt 4266   cdm 4878  cfv 5454  (class class class)co 6081   cmpt2 6083   cof 6303 This theorem is referenced by:  psrval  16429  resspsradd  16479  resspsrvsca  16481  sitmval  24661  mendval  27468  mendplusgfval  27470  mendvscafval  27475  ldualset  29923 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-iota 5418  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-of 6305
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