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Theorem hbxfr 98
Description: Transfer a hypothesis builder to an equivalent expression.
Hypotheses
Ref Expression
hbxfr.1 |- T:be
hbxfr.2 |- B:al
hbxfr.3 |- R |= [T = A]
hbxfr.4 |- R |= [(\x:al AB) = A]
Assertion
Ref Expression
hbxfr |- R |= [(\x:al TB) = T]
Distinct variable group:   x,R
Proof of Theorem hbxfr
StepHypRef Expression
1 hbxfr.3 . . . 4 |- R |= [T = A]
21ax-cb1 29 . . 3 |- R:*
32id 25 . 2 |- R |= R
4 hbxfr.1 . . 3 |- T:be
5 hbxfr.2 . . 3 |- B:al
6 hbxfr.4 . . . 4 |- R |= [(\x:al AB) = A]
76, 2adantr 50 . . 3 |- (R, R) |= [(\x:al AB) = A]
84, 5, 1, 7hbxfrf 97 . 2 |- (R, R) |= [(\x:al TB) = T]
93, 3, 8syl2anc 19 1 |- R |= [(\x:al TB) = T]
Colors of variables: type var term
Syntax hints:  kc 5  \kl 6   = ke 7  [kbr 9   |= wffMMJ2 11  wffMMJ2t 12
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-ceq 46  ax-leq 62
This theorem depends on definitions:  df-ov 65
This theorem is referenced by:  hbth  99
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