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Theorem trul 39
Description: Deduction form of tru 44. (Contributed by Mario Carneiro, 7-Oct-2014.)
Hypothesis
Ref Expression
trul.1 (⊤, R)⊧S
Assertion
Ref Expression
trul RS

Proof of Theorem trul
StepHypRef Expression
1 trul.1 . . . . 5 (⊤, R)⊧S
21ax-cb1 29 . . . 4 (⊤, R):∗
32wctr 34 . . 3 R:∗
43trud 27 . 2 R⊧⊤
53id 25 . 2 RR
64, 5, 1syl2anc 19 1 RS
Colors of variables: type var term
Syntax hints:  kt 8  kct 10  wffMMJ2 11
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-id 24  ax-trud 26  ax-cb1 29  ax-wctr 32
This theorem is referenced by:  alnex  186  exnal1  187
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