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Theorem eximdv 173
Description: Deduction from Theorem 19.22 of [Margaris] p. 90.
Hypothesis
Ref Expression
alimdv.1 (R, A)⊧B
Assertion
Ref Expression
eximdv (R, (λx:α A))⊧(λx:α B)
Distinct variable groups:   x,R   α,x

Proof of Theorem eximdv
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 alimdv.1 . . 3 (R, A)⊧B
21ax-cb2 30 . . . 4 B:∗
3219.8a 160 . . 3 B⊧(λx:α B)
41, 3syl 16 . 2 (R, A)⊧(λx:α B)
51ax-cb1 29 . . . 4 (R, A):∗
65wctl 31 . . 3 R:∗
7 wv 58 . . 3 y:α:α
86, 7ax-17 95 . 2 ⊤⊧[(λx:α Ry:α) = R]
9 wex 129 . . 3 :((α → ∗) → ∗)
102wl 59 . . 3 λx:α B:(α → ∗)
119, 7ax-17 95 . . 3 ⊤⊧[(λx:α y:α) = ]
122, 7ax-hbl1 93 . . 3 ⊤⊧[(λx:α λx:α By:α) = λx:α B]
139, 10, 7, 11, 12hbc 100 . 2 ⊤⊧[(λx:α (λx:α B)y:α) = (λx:α B)]
144, 8, 13exlimd 171 1 (R, (λx:α A))⊧(λx:α B)
Colors of variables: type var term
Syntax hints:  tv 1  ht 2  hb 3  kc 5  λkl 6  kt 8  kct 10  wffMMJ2 11  tex 113
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-id 24  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-refl 39  ax-eqmp 42  ax-ded 43  ax-ceq 46  ax-beta 60  ax-distrc 61  ax-leq 62  ax-distrl 63  ax-hbl1 93  ax-17 95  ax-inst 103
This theorem depends on definitions:  df-ov 65  df-al 116  df-an 118  df-im 119  df-ex 121
This theorem is referenced by: (None)
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