Theorem ofeq 6542

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.

Step	Hyp	Ref	Expression
1		simp1 996	. . . . 5
2	1	oveqd 6313	. . . 4
3	2	mpteq2dv 4539	. . 3
4	3	mpt2eq3dva 6361	. 2
5		df-of 6540	. 2
6		df-of 6540	. 2
7	4, 5, 6	3eqtr4g 2523	1

Syntax hints:  ->wi 4  /\w3a 973  =wceq 1395  e.wcel 1818  cvv 3109  i^icin 3474  e.cmpt 4510  domcdm 5004  `cfv 5593  (class class class)co 6296  e.cmpt2 6298  oFcof 6538

This theorem is referenced by:  psrval  18011  resspsradd  18071  resspsrvsca  18073  sitmval  28290  mendval  31132  mendplusgfval  31134  mendvscafval  31139  ldualset  34850

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  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-ral 2812  df-rex 2813  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-iota 5556  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-of 6540