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Theorem exbid 1773
Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
exbid.1 xφ
exbid.2 (φ → (ψχ))
Assertion
Ref Expression
exbid (φ → (xψxχ))

Proof of Theorem exbid
StepHypRef Expression
1 exbid.1 . . 3 xφ
21nfri 1762 . 2 (φxφ)
3 exbid.2 . 2 (φ → (ψχ))
42, 3exbidh 1591 1 (φ → (xψxχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wex 1541  wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  mobid  2238  rexbida  2629  rexeqf  2804  opabbid  4624  dfid3  4768  oprabbid  5563
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