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Theorem spimed 1977
 Description: Deduction version of spime 1976. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
spimed.1 (χ → Ⅎxφ)
spimed.2 (x = y → (φψ))
Assertion
Ref Expression
spimed (χ → (φxψ))

Proof of Theorem spimed
StepHypRef Expression
1 spimed.1 . 2 (χ → Ⅎxφ)
2 nfnf1 1790 . . . . 5 xxφ
3 id 19 . . . . 5 (Ⅎxφ → Ⅎxφ)
42, 3nfan1 1881 . . . 4 x(Ⅎxφ φ)
5 spimed.2 . . . . 5 (x = y → (φψ))
65adantld 453 . . . 4 (x = y → ((Ⅎxφ φ) → ψ))
74, 6spime 1976 . . 3 ((Ⅎxφ φ) → xψ)
87ex 423 . 2 (Ⅎxφ → (φxψ))
91, 8syl 15 1 (χ → (φxψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358  ∃wex 1541  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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  equvini  1987
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