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Theorem anasss 61
Description: Associativity for context. (Contributed by Mario Carneiro, 8-Oct-2014.)
Hypothesis
Ref Expression
an32s.1 |- ((R, S), T) |= A
Assertion
Ref Expression
anasss |- (R, (S, T)) |= A

Proof of Theorem anasss
StepHypRef Expression
1 an32s.1 . . . . . . . 8 |- ((R, S), T) |= A
21ax-cb1 29 . . . . . . 7 |- ((R, S), T):*
32wctl 33 . . . . . 6 |- (R, S):*
43id 25 . . . . 5 |- (R, S) |= (R, S)
54ancoms 54 . . . 4 |- (S, R) |= (R, S)
65, 1sylan 59 . . 3 |- ((S, R), T) |= A
76an32s 60 . 2 |- ((S, T), R) |= A
87ancoms 54 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-id 24  ax-cb1 29  ax-wctl 31  ax-wctr 32
This theorem is referenced by: (None)
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