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Theorem insti 104
Description: Instantiate a theorem with a new term.
Hypotheses
Ref Expression
insti.1 |- C:al
insti.2 |- B:*
insti.3 |- R |= A
insti.4 |- T. |= [(\x:al By:al) = B]
insti.5 |- [x:al = C] |= [A = B]
Assertion
Ref Expression
insti |- R |= B
Distinct variable groups:   x,y,R   y,B
Proof of Theorem insti
StepHypRef Expression
1 insti.3 . 2 |- R |= A
2 insti.4 . 2 |- T. |= [(\x:al By:al) = B]
31ax-cb1 29 . . 3 |- R:*
4 wv 58 . . 3 |- y:al:al
53, 4ax-17 95 . 2 |- T. |= [(\x:al Ry:al) = R]
6 insti.5 . 2 |- [x:al = C] |= [A = B]
76ax-cb1 29 . . 3 |- [x:al = C]:*
87, 3eqid 73 . 2 |- [x:al = C] |= [R = R]
91, 2, 5, 6, 8ax-inst 103 1 |- R |= B
Colors of variables: type var term
Syntax hints:  tv 1  *hb 3  kc 5  \kl 6   = ke 7  T.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-refl 39  ax-eqmp 42  ax-ceq 46  ax-17 95  ax-inst 103
This theorem depends on definitions:  df-ov 65
This theorem is referenced by:  clf  105  exlimdv  157  cbvf  167  exlimd  171
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