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Theorem alrimdd 1768
 Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
alrimdd.1 xφ
alrimdd.2 (φ → Ⅎxψ)
alrimdd.3 (φ → (ψχ))
Assertion
Ref Expression
alrimdd (φ → (ψxχ))

Proof of Theorem alrimdd
StepHypRef Expression
1 alrimdd.2 . . 3 (φ → Ⅎxψ)
21nfrd 1763 . 2 (φ → (ψxψ))
3 alrimdd.1 . . 3 xφ
4 alrimdd.3 . . 3 (φ → (ψχ))
53, 4alimd 1764 . 2 (φ → (xψxχ))
62, 5syld 40 1 (φ → (ψxχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 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:  alrimd  1769  19.23tOLD  1819
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