Theorem bdnthALT 15589

Description: Alternate proof of bdnth 15588 not using bdfal 15587. Then, bdfal 15587 can be proved from this theorem, using fal 1371. The total number of proof steps would be 17 (for bdnthALT 15589) + 3 = 20, which is more than 8 (for bdfal 15587) + 9 (for bdnth 15588) = 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 15586	. . 3 |- BOUNDED T.
2	1	ax-bdn 15571	. 2 |- BOUNDED -. T.
3		notnot 630	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1373	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 702	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 15578	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1365  BOUNDED wbd 15566

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 615  ax-in2 616  ax-bd0 15567  ax-bdim 15568  ax-bdn 15571  ax-bdeq 15574

This theorem depends on definitions:  df-bi 117  df-tru 1367

This theorem is referenced by: (None)