Theorem modal-b 1026

Description: The analog in our "pure" predicate calculus of the Brouwer axiom (B) of modal logic S5.

Assertion

Ref	Expression
modal-b	|- (ph -> A.x -. A.x -. ph)

Proof of Theorem modal-b

Step	Hyp	Ref	Expression
1		ax-6o 976	. 2 |- (-. A.x -. A.x -. ph -> -. ph)
2	1	a3i 74	1 |- (ph -> A.x -. A.x -. ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 952

This theorem is referenced by:  ax9 1122

This theorem was proved from axioms:  ax-3 6  ax-mp 7  ax-6o 976

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