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Theorem beta 92
 Description: Axiom of beta-substitution. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
beta.1 A:β
Assertion
Ref Expression
beta ⊤⊧[(λx:α Ax:α) = A]

Proof of Theorem beta
StepHypRef Expression
1 weq 41 . 2 = :(β → (β → ∗))
2 beta.1 . . . 4 A:β
32wl 66 . . 3 λx:α A:(αβ)
4 wv 64 . . 3 x:α:α
53, 4wc 50 . 2 (λx:α Ax:α):β
62ax-beta 67 . 2 ⊤⊧(( = (λx:α Ax:α))A)
71, 5, 2, 6dfov2 75 1 ⊤⊧[(λx:α Ax:α) = A]
 Colors of variables: type var term Syntax hints:  tv 1  kc 5  λkl 6   = ke 7  ⊤kt 8  [kbr 9  ⊧wffMMJ2 11  wffMMJ2t 12 This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-trud 26  ax-cb1 29  ax-cb2 30  ax-weq 40  ax-refl 42  ax-eqmp 45  ax-wc 49  ax-ceq 51  ax-wv 63  ax-wl 65  ax-beta 67  ax-wov 71 This theorem depends on definitions:  df-ov 73 This theorem is referenced by:  clf  115  ax4  150  exlimdv  167  19.8a  170  cbvf  179  leqf  181  exlimd  183  ax11  214  axrep  220
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