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Theorem hbim 1410
Description: If is not free in and , it is not free in . (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 3-Mar-2008.) (Revised by Mario Carneiro, 2-Feb-2015.)
Hypotheses
Ref Expression
hb.1
hb.2
Assertion
Ref Expression
hbim

Proof of Theorem hbim
StepHypRef Expression
1 ax-4 1373 . . 3
2 hb.2 . . 3
31, 2imim12i 53 . 2
4 ax-i5r 1401 . 2
5 hb.1 . . . 4
65imim1i 54 . . 3
76alimi 1317 . 2
83, 4, 73syl 17 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1221
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1309  ax-gen 1311  ax-4 1373  ax-i5r 1401
This theorem is referenced by:  hbbi  1413  hbia1  1417  19.21h  1422  19.38  1539  hbsbv  1790  hbmo1  1911  hbmo  1912  moexexdc  1957  2eu4  1966  cleqh  2110  hbral  2322
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