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Theorem rgenm 3317
Description: Generalization rule that eliminates an inhabited class requirement. (Contributed by Jim Kingdon, 5-Aug-2018.)
Hypothesis
Ref Expression
rgenm.1
Assertion
Ref Expression
rgenm
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem rgenm
StepHypRef Expression
1 nfe1 1382 . . . . 5  F/
2 rgenm.1 . . . . . 6
32ex 108 . . . . 5
41, 3alrimi 1412 . . . 4
5 19.38 1563 . . . 4
64, 5ax-mp 7 . . 3
7 pm5.4 238 . . . 4
87albii 1356 . . 3
96, 8mpbi 133 . 2
10 df-ral 2305 . 2
119, 10mpbir 134 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240  wex 1378   wcel 1390  wral 2300
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-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by: (None)
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