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Theorem hbex 1524
Description: If x is not free in φ, it is not free in yφ. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
Hypothesis
Ref Expression
hbex.1 (φxφ)
Assertion
Ref Expression
hbex (yφxyφ)

Proof of Theorem hbex
StepHypRef Expression
1 hbe1 1381 . . 3 (yφyyφ)
21hbal 1363 . 2 (xyφyxyφ)
3 hbex.1 . . 3 (φxφ)
4 19.8a 1479 . . 3 (φyφ)
53, 4alrimih 1355 . 2 (φxyφ)
62, 5exlimih 1481 1 (yφxyφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wex 1378
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-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  nfex  1525  excomim  1550  19.12  1552  cbvexh  1635  cbvexdh  1798  hbsbv  1814  hbeu1  1907  hbmo  1936  moexexdc  1981
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