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Theorem alimd 1764
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alimd.1 xφ
alimd.2 (φ → (ψχ))
Assertion
Ref Expression
alimd (φ → (xψxχ))

Proof of Theorem alimd
StepHypRef Expression
1 alimd.1 . . 3 xφ
21nfri 1762 . 2 (φxφ)
3 alimd.2 . 2 (φ → (ψχ))
42, 3alimdh 1563 1 (φ → (xψxχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wnf 1544
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  alrimdd  1768  nfimdOLD  1809  spimt  1974  sbied  2036  sb9i  2094  mo  2226  2mo  2282  ralimdaa  2691
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