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Theorem anassrs 62
Description: Associativity for context. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
anassrs.1 (R, (S, T))⊧A
Assertion
Ref Expression
anassrs ((R, S), T)⊧A

Proof of Theorem anassrs
StepHypRef Expression
1 anassrs.1 . . . . . 6 (R, (S, T))⊧A
21ax-cb1 29 . . . . 5 (R, (S, T)):∗
32wctl 33 . . . 4 R:∗
42wctr 34 . . . . 5 (S, T):∗
54wctl 33 . . . 4 S:∗
63, 5simpl 22 . . 3 (R, S)⊧R
74wctr 34 . . 3 T:∗
86, 7adantr 55 . 2 ((R, S), T)⊧R
93, 5simpr 23 . . 3 (R, S)⊧S
109, 7ct1 57 . 2 ((R, S), T)⊧(S, T)
118, 10, 1syl2anc 19 1 ((R, S), T)⊧A
Colors of variables: type var term
Syntax hints:  kct 10  wffMMJ2 11
This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-cb1 29  ax-wctl 31  ax-wctr 32
This theorem is referenced by: (None)
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