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Theorem uniss2 3611
 Description: A subclass condition on the members of two classes that implies a subclass relation on their unions. Proposition 8.6 of [TakeutiZaring] p. 59. (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
uniss2
Distinct variable groups:   ,   ,,
Allowed substitution hint:   ()

Proof of Theorem uniss2
StepHypRef Expression
1 ssuni 3602 . . . . 5
21expcom 109 . . . 4
32rexlimiv 2427 . . 3
43ralimi 2384 . 2
5 unissb 3610 . 2
64, 5sylibr 137 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1393  wral 2306  wrex 2307   wss 2917  cuni 3580 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-in 2924  df-ss 2931  df-uni 3581 This theorem is referenced by:  unidif  3612
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