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Theorem 19.9d 1782
Description: A deduction version of one direction of 19.9 1783. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.9d.1 (ψ → Ⅎxφ)
Assertion
Ref Expression
19.9d (ψ → (xφφ))

Proof of Theorem 19.9d
StepHypRef Expression
1 19.9d.1 . . 3 (ψ → Ⅎxφ)
2 19.9t 1779 . . 3 (Ⅎxφ → (xφφ))
31, 2syl 15 . 2 (ψ → (xφφ))
43biimpd 198 1 (ψ → (xφφ))
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-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  exdistrf  1971  sbied  2036  sbequi  2059  copsexg  4607
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