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Theorem simprd 38
Description: Extract an assumption from the context. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
simpld.1 |- R |= (S, T)
Assertion
Ref Expression
simprd |- R |= T

Proof of Theorem simprd
StepHypRef Expression
1 simpld.1 . 2 |- R |= (S, T)
21ax-cb2 30 . . . 4 |- (S, T):*
32wctl 33 . . 3 |- S:*
42wctr 34 . . 3 |- T:*
53, 4simpr 23 . 2 |- (S, T) |= T
61, 5syl 16 1 |- R |= T
Colors of variables: type var term
Syntax hints:  kct 10   |= wffMMJ2 11
This theorem was proved from axioms:  ax-syl 15  ax-simpr 21  ax-cb2 30  ax-wctl 31  ax-wctr 32
This theorem is referenced by:  mpd  156  exmid  199  ax2  204
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