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Theorem eximdh 1499
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.)
Hypotheses
Ref Expression
eximdh.1 (φxφ)
eximdh.2 (φ → (ψχ))
Assertion
Ref Expression
eximdh (φ → (xψxχ))

Proof of Theorem eximdh
StepHypRef Expression
1 eximdh.1 . . 3 (φxφ)
2 eximdh.2 . . 3 (φ → (ψχ))
31, 2alrimih 1355 . 2 (φx(ψχ))
4 exim 1487 . 2 (x(ψχ) → (xψxχ))
53, 4syl 14 1 (φ → (xψxχ))
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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  eximd  1500  19.41h  1572  hbexd  1581  equsex  1613  equsexd  1614  spimeh  1624  sbiedh  1667  exdistrfor  1678  eximdv  1757  cbvexdh  1798  mopick2  1980  2euex  1984  bj-sbimedh  9226
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