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Theorem ralab2 2872
 Description: Universal quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
ralab2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ralab2
StepHypRef Expression
1 df-ral 2437 . 2
2 nfsab1 2144 . . . 4
3 nfv 1505 . . . 4
42, 3nfim 1549 . . 3
5 nfv 1505 . . 3
6 eleq1 2217 . . . . 5
7 abid 2142 . . . . 5
86, 7bitrdi 195 . . . 4
9 ralab2.1 . . . 4
108, 9imbi12d 233 . . 3
114, 5, 10cbval 1731 . 2
121, 11bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330   wcel 2125  cab 2140  wral 2432 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-ral 2437 This theorem is referenced by:  ralrab2  2873  ssintab  3820
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