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Theorem ofeq 6541
 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 996 . . . . 5
21oveqd 6313 . . . 4
32mpteq2dv 4544 . . 3
43mpt2eq3dva 6360 . 2
5 df-of 6539 . 2
6 df-of 6539 . 2
74, 5, 63eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 973   wceq 1395   wcel 1819  cvv 3109   cin 3470   cmpt 4515   cdm 5008  cfv 5594  (class class class)co 6296   cmpt2 6298   cof 6537 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-uni 4252  df-br 4457  df-opab 4516  df-mpt 4517  df-iota 5557  df-fv 5602  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-of 6539 This theorem is referenced by:  psrval  18137  resspsradd  18197  resspsrvsca  18199  sitmval  28465  mendval  31294  mendplusgfval  31296  mendvscafval  31301  ldualset  34951
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