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Theorem 19.8a 160
Description: Existential introduction.
Hypothesis
Ref Expression
19.8a.1 |- A:*
Assertion
Ref Expression
19.8a |- A |= (E.\x:al A)
Proof of Theorem 19.8a
StepHypRef Expression
1 19.8a.1 . . . 4 |- A:*
21ax-id 24 . . 3 |- A |= A
31beta 82 . . . 4 |- T. |= [(\x:al Ax:al) = A]
41, 3a1i 28 . . 3 |- A |= [(\x:al Ax:al) = A]
52, 4mpbir 77 . 2 |- A |= (\x:al Ax:al)
61wl 59 . . 3 |- \x:al A:(al -> *)
7 wv 58 . . 3 |- x:al:al
86, 7ax4e 158 . 2 |- (\x:al Ax:al) |= (E.\x:al A)
95, 8syl 16 1 |- A |= (E.\x:al A)
Colors of variables: type var term
Syntax hints:  tv 1  *hb 3  kc 5  \kl 6   = ke 7  [kbr 9   |= wffMMJ2 11  wffMMJ2t 12  E.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:  eximdv  173  alnex  174  ax9  199
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