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Theorem hbl1 104
Description: Inference form of ax-hbl1 103. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypotheses
Ref Expression
ax-hbl1.1 |- A:ga
ax-hbl1.2 |- B:al
hbl1.3 |- R:*
Assertion
Ref Expression
hbl1 |- R |= [(\x:al \x:be AB) = \x:be A]

Proof of Theorem hbl1
StepHypRef Expression
1 hbl1.3 . 2 |- R:*
2 ax-hbl1.1 . . 3 |- A:ga
3 ax-hbl1.2 . . 3 |- B:al
42, 3ax-hbl1 103 . 2 |- T. |= [(\x:al \x:be AB) = \x:be A]
51, 4a1i 28 1 |- R |= [(\x:al \x:be AB) = \x:be A]
Colors of variables: type var term
Syntax hints:  *hb 3  kc 5  \kl 6   = ke 7  [kbr 9   |= wffMMJ2 11  wffMMJ2t 12
This theorem was proved from axioms:  ax-syl 15  ax-trud 26  ax-hbl1 103
This theorem is referenced by:  clf  115  cbvf  179  axrep  220
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