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Theorem ofeq 5742
 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 915 . . . . 5
21oveqd 5557 . . . 4
32mpteq2dv 3876 . . 3
43mpt2eq3dva 5597 . 2
5 df-of 5740 . 2
6 df-of 5740 . 2
74, 5, 63eqtr4g 2113 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 896   wceq 1259   wcel 1409  cvv 2574   cin 2944   cmpt 3846   cdm 4373  cfv 4930  (class class class)co 5540   cmpt2 5542   cof 5738 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-uni 3609  df-br 3793  df-opab 3847  df-mpt 3848  df-iota 4895  df-fv 4938  df-ov 5543  df-oprab 5544  df-mpt2 5545  df-of 5740 This theorem is referenced by: (None)
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