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Theorem a17i 106
Description: Inference form of ax-17 105. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
ax-17.1 A:β
ax-17.2 B:α
a17i.3 R:∗
Assertion
Ref Expression
a17i R⊧[(λx:α AB) = A]
Distinct variable group:   x,A

Proof of Theorem a17i
StepHypRef Expression
1 a17i.3 . 2 R:∗
2 ax-17.1 . . 3 A:β
3 ax-17.2 . . 3 B:α
42, 3ax-17 105 . 2 ⊤⊧[(λx:α AB) = A]
51, 4a1i 28 1 R⊧[(λx:α AB) = A]
Colors of variables: type var term
Syntax hints:  hb 3  kc 5  λkl 6   = ke 7  [kbr 9  wffMMJ2 11  wffMMJ2t 12
This theorem was proved from axioms:  ax-syl 15  ax-trud 26  ax-17 105
This theorem is referenced by:  hbth  109  clf  115  hbct  155  axun  222
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