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Theorem an32s 60
 Description: Commutation identity for context. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
an32s.1 ((R, S), T)⊧A
Assertion
Ref Expression
an32s ((R, T), S)⊧A

Proof of Theorem an32s
StepHypRef Expression
1 an32s.1 . . . . . . 7 ((R, S), T)⊧A
21ax-cb1 29 . . . . . 6 ((R, S), T):∗
32wctl 33 . . . . 5 (R, S):∗
43wctl 33 . . . 4 R:∗
52wctr 34 . . . 4 T:∗
64, 5simpl 22 . . 3 (R, T)⊧R
73wctr 34 . . 3 S:∗
86, 7ct1 57 . 2 ((R, T), S)⊧(R, S)
94, 5simpr 23 . . 3 (R, T)⊧T
109, 7adantr 55 . 2 ((R, T), S)⊧T
118, 10, 1syl2anc 19 1 ((R, T), S)⊧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:  anasss  61  con2d  161  ax3  205
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