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Theorem ded 74
Description: Deduction theorem for equality.
Hypotheses
Ref Expression
ded.1 |- (R, S) |= T
ded.2 |- (R, T) |= S
Assertion
Ref Expression
ded |- R |= [S = T]

Proof of Theorem ded
StepHypRef Expression
1 weq 38 . 2 |- = :(* -> (* -> *))
2 ded.2 . . 3 |- (R, T) |= S
32ax-cb2 30 . 2 |- S:*
4 ded.1 . . 3 |- (R, S) |= T
54ax-cb2 30 . 2 |- T:*
64, 2ax-ded 43 . 2 |- R |= (( = S)T)
71, 3, 5, 6dfov2 67 1 |- R |= [S = T]
Colors of variables: type var term
Syntax hints:  *hb 3   = ke 7  [kbr 9  kct 10   |= wffMMJ2 11
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-ded 43  ax-ceq 46
This theorem depends on definitions:  df-ov 65
This theorem is referenced by:  dedi  75  eqtru  76  ex  148  notval2  149  dfex2  185
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