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Theorem toponunii 13377
Description: The base set of a topology on a given base set. (Contributed by Mario Carneiro, 13-Aug-2015.)
Hypothesis
Ref Expression
topontopi.1 𝐽 ∈ (TopOnβ€˜π΅)
Assertion
Ref Expression
toponunii 𝐡 = βˆͺ 𝐽

Proof of Theorem toponunii
StepHypRef Expression
1 topontopi.1 . 2 𝐽 ∈ (TopOnβ€˜π΅)
2 toponuni 13375 . 2 (𝐽 ∈ (TopOnβ€˜π΅) β†’ 𝐡 = βˆͺ 𝐽)
31, 2ax-mp 5 1 𝐡 = βˆͺ 𝐽
Colors of variables: wff set class
Syntax hints:   = wceq 1353   ∈ wcel 2148  βˆͺ cuni 3809  β€˜cfv 5214  TopOnctopon 13370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-sep 4120  ax-pow 4173  ax-pr 4208  ax-un 4432
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-rab 2464  df-v 2739  df-sbc 2963  df-un 3133  df-in 3135  df-ss 3142  df-pw 3577  df-sn 3598  df-pr 3599  df-op 3601  df-uni 3810  df-br 4003  df-opab 4064  df-mpt 4065  df-id 4292  df-xp 4631  df-rel 4632  df-cnv 4633  df-co 4634  df-dm 4635  df-iota 5176  df-fun 5216  df-fv 5222  df-topon 13371
This theorem is referenced by:  toponrestid  13381  unicntopcntop  13898  reldvg  14010  dvidlemap  14022  dvcnp2cntop  14025  dvaddxxbr  14027  dvmulxxbr  14028  dvcoapbr  14033
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