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Theorem exbidh 1502
Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
exbidh.1 (φxφ)
exbidh.2 (φ → (ψχ))
Assertion
Ref Expression
exbidh (φ → (xψxχ))

Proof of Theorem exbidh
StepHypRef Expression
1 exbidh.1 . . 3 (φxφ)
2 exbidh.2 . . 3 (φ → (ψχ))
31, 2alrimih 1355 . 2 (φx(ψχ))
4 exbi 1492 . 2 (x(ψχ) → (xψxχ))
53, 4syl 14 1 (φ → (xψxχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  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:  exbid  1504  drex2  1617  drex1  1676  exbidv  1703  mobidh  1931
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