Theorem bj-trst 15385

Description: A provable formula is stable. (Contributed by BJ, 24-Nov-2023.)

Assertion

Ref	Expression
bj-trst	|- ( ph -> STAB ph )

Proof of Theorem bj-trst

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( ph -> ( -. -. ph -> ph ) )
2		df-stab 832	. 2 |- (STAB ph <-> ( -. -. ph -> ph ) )
3	1, 2	sylibr 134	1 |- ( ph -> STAB ph )

Syntax hints:   -. wn 3   -> wi 4  STAB wstab 831

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-stab 832

This theorem is referenced by:  bj-sttru  15386  bj-nnst  15389  bj-nnbist  15390  bj-dcstab  15402