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Theorem hbimd 1815
 Description: Deduction form of bound-variable hypothesis builder hbim 1817. (Contributed by NM, 1-Jan-2002.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)
Hypotheses
Ref Expression
hbimd.1 (φxφ)
hbimd.2 (φ → (ψxψ))
hbimd.3 (φ → (χxχ))
Assertion
Ref Expression
hbimd (φ → ((ψχ) → x(ψχ)))

Proof of Theorem hbimd
StepHypRef Expression
1 hbimd.1 . . . 4 (φxφ)
2 hbimd.2 . . . 4 (φ → (ψxψ))
31, 2nfdh 1767 . . 3 (φ → Ⅎxψ)
4 hbimd.3 . . . 4 (φ → (χxχ))
51, 4nfdh 1767 . . 3 (φ → Ⅎxχ)
63, 5nfimd 1808 . 2 (φ → Ⅎx(ψχ))
76nfrd 1763 1 (φ → ((ψχ) → x(ψχ)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540 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-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  spimehOLD  1821  dvelimhw  1849  dvelimv  1939  dvelimh  1964  dvelimALT  2133  dvelimf-o  2180
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