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Theorem simpld 37
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
simpld |- R |= S

Proof of Theorem simpld
StepHypRef Expression
1 simpld.1 . 2 |- R |= (S, T)
21ax-cb2 30 . . . 4 |- (S, T):*
32wctl 33 . . 3 |- S:*
42wctr 34 . . 3 |- T:*
53, 4simpl 22 . 2 |- (S, T) |= S
61, 5syl 16 1 |- R |= S
Colors of variables: type var term
Syntax hints:  kct 10   |= wffMMJ2 11
This theorem was proved from axioms:  ax-syl 15  ax-simpl 20  ax-cb2 30  ax-wctl 31  ax-wctr 32
This theorem is referenced by:  ex  158  exmid  199  ax2  204
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