Theorem bdnthALT 15481

Description: Alternate proof of bdnth 15480 not using bdfal 15479. Then, bdfal 15479 can be proved from this theorem, using fal 1371. The total number of proof steps would be 17 (for bdnthALT 15481) + 3 = 20, which is more than 8 (for bdfal 15479) + 9 (for bdnth 15480) = 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 15478	. . 3 |- BOUNDED T.
2	1	ax-bdn 15463	. 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 15470	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1365  BOUNDED wbd 15458

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 15459  ax-bdim 15460  ax-bdn 15463  ax-bdeq 15466

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

This theorem is referenced by: (None)