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Theorem 19.8a 170
Description: Existential introduction. (Contributed by Mario Carneiro, 9-Oct-2014.)
Hypothesis
Ref Expression
19.8a.1 A:∗
Assertion
Ref Expression
19.8a A⊧(λx:α A)

Proof of Theorem 19.8a
StepHypRef Expression
1 19.8a.1 . . . 4 A:∗
21ax-id 24 . . 3 AA
31beta 92 . . . 4 ⊤⊧[(λx:α Ax:α) = A]
41, 3a1i 28 . . 3 A⊧[(λx:α Ax:α) = A]
52, 4mpbir 87 . 2 A⊧(λx:α Ax:α)
61wl 66 . . 3 λx:α A:(α → ∗)
7 wv 64 . . 3 x:α:α
86, 7ax4e 168 . 2 (λx:α Ax:α)⊧(λx:α A)
95, 8syl 16 1 A⊧(λx:α A)
Colors of variables: type var term
Syntax hints:  tv 1  hb 3  kc 5  λkl 6   = ke 7  [kbr 9  wffMMJ2 11  wffMMJ2t 12  tex 123
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-wctl 31  ax-wctr 32  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-ded 46  ax-wct 47  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-distrc 68  ax-leq 69  ax-distrl 70  ax-wov 71  ax-eqtypi 77  ax-eqtypri 80  ax-hbl1 103  ax-17 105  ax-inst 113
This theorem depends on definitions:  df-ov 73  df-al 126  df-an 128  df-im 129  df-ex 131
This theorem is referenced by:  eximdv  185  alnex  186  ax9  212
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