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Theorem mptun 5567
 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 4260 . 2
2 df-mpt 4260 . . . 4
3 df-mpt 4260 . . . 4
42, 3uneq12i 3491 . . 3
5 elun 3480 . . . . . . 7
65anbi1i 677 . . . . . 6
7 andir 839 . . . . . 6
86, 7bitri 241 . . . . 5
98opabbii 4264 . . . 4
10 unopab 4276 . . . 4
119, 10eqtr4i 2458 . . 3
124, 11eqtr4i 2458 . 2
131, 12eqtr4i 2458 1
 Colors of variables: wff set class Syntax hints:   wo 358   wa 359   wceq 1652   wcel 1725   cun 3310  copab 4257   cmpt 4258 This theorem is referenced by:  fmptap  5915  fmptapd  24053  partfun  24079 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-opab 4259  df-mpt 4260
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