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Theorem ofeq 6484
 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 1005 . . . . 5
21oveqd 6259 . . . 4
32mpteq2dv 4447 . . 3
43mpt2eq3dva 6306 . 2
5 df-of 6482 . 2
6 df-of 6482 . 2
74, 5, 63eqtr4g 2481 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 982   wceq 1437   wcel 1872  cvv 3016   cin 3371   cmpt 4418   cdm 4789  cfv 5537  (class class class)co 6242   cmpt2 6244   cof 6480 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2402 This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2552  df-ral 2713  df-rex 2714  df-uni 4156  df-br 4360  df-opab 4419  df-mpt 4420  df-iota 5501  df-fv 5545  df-ov 6245  df-oprab 6246  df-mpt2 6247  df-of 6482 This theorem is referenced by:  psrval  18522  resspsradd  18576  resspsrvsca  18578  sitmval  29127  ldualset  32597  mendval  35956  mendplusgfval  35958  mendvscafval  35963
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