Theorem bdnthALT 14626

Description: Alternate proof of bdnth 14625 not using bdfal 14624. Then, bdfal 14624 can be proved from this theorem, using fal 1360. The total number of proof steps would be 17 (for bdnthALT 14626) + 3 = 20, which is more than 8 (for bdfal 14624) + 9 (for bdnth 14625) = 17. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bdnth.1	|- -. ph

Assertion

Ref	Expression
bdnthALT	|- BOUNDED ph

Proof of Theorem bdnthALT

Step	Hyp	Ref	Expression
1		bdtru 14623	. . 3 |- BOUNDED T.
2	1	ax-bdn 14608	. 2 |- BOUNDED -. T.
3		notnot 629	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1362	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 701	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 14615	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1354  BOUNDED wbd 14603

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-bd0 14604  ax-bdim 14605  ax-bdn 14608  ax-bdeq 14611

This theorem depends on definitions:  df-bi 117  df-tru 1356

This theorem is referenced by: (None)