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Theorem iunconALT 29048
 Description: The indexed union of connected overlapping subspaces sharing a common point is connected. This proof was automatically derived by completeusersproof from its Virtual Deduction proof counterpart http://www.virtualdeduction.com/iunconaltvd.html. As it is verified by the Metamath program, iunconALT 29048 verifies http://www.virtualdeduction.com/iunconaltvd.html. (Contributed by Alan Sare, 22-Apr-2018.)
Hypotheses
Ref Expression
iunconALT.1 TopOn
iunconALT.2
iunconALT.3
iunconALT.4 t
Assertion
Ref Expression
iunconALT t
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iunconALT
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 biid 228 . 2
2 iunconALT.1 . 2 TopOn
3 iunconALT.2 . 2
4 iunconALT.3 . 2
5 iunconALT.4 . 2 t
61, 2, 3, 4, 5iunconlem2 29047 1 t
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725   wne 2599   cdif 3317   cun 3318   cin 3319   wss 3320  c0 3628  ciun 4093  cfv 5454  (class class class)co 6081   ↾t crest 13648  TopOnctopon 16959  ccon 17474 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-int 4051  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-tr 4303  df-eprel 4494  df-id 4498  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585  df-lim 4586  df-suc 4587  df-om 4846  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350  df-recs 6633  df-rdg 6668  df-oadd 6728  df-er 6905  df-en 7110  df-fin 7113  df-fi 7416  df-rest 13650  df-topgen 13667  df-top 16963  df-bases 16965  df-topon 16966  df-cld 17083  df-con 17475
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