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Theorem mptun 5665
 Description: Union of mappings which are mutually compatible. (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
mptun

Proof of Theorem mptun
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt 4422 . 2
2 df-mpt 4422 . . . 4
3 df-mpt 4422 . . . 4
42, 3uneq12i 3556 . . 3
5 elun 3544 . . . . . . 7
65anbi1i 699 . . . . . 6
7 andir 876 . . . . . 6
86, 7bitri 252 . . . . 5
98opabbii 4426 . . . 4
10 unopab 4437 . . . 4
119, 10eqtr4i 2448 . . 3
124, 11eqtr4i 2448 . 2
131, 12eqtr4i 2448 1
 Colors of variables: wff setvar class Syntax hints:   wo 369   wa 370   wceq 1437   wcel 1872   cun 3372  copab 4419   cmpt 4420 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 2403 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2410  df-cleq 2416  df-clel 2419  df-nfc 2553  df-v 3019  df-un 3379  df-opab 4421  df-mpt 4422 This theorem is referenced by:  fmptap  6041  fmptapd  6042  partfun  28219  esumrnmpt2  28836  ptrest  31846
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