Theorem bdnthALT 16481

Description: Alternate proof of bdnth 16480 not using bdfal 16479. Then, bdfal 16479 can be proved from this theorem, using fal 1404. The total number of proof steps would be 17 (for bdnthALT 16481) + 3 = 20, which is more than 8 (for bdfal 16479) + 9 (for bdnth 16480) = 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 16478	. . 3 |- BOUNDED T.
2	1	ax-bdn 16463	. 2 |- BOUNDED -. T.
3		notnot 634	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1406	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 708	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 16470	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1398  BOUNDED wbd 16458

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 619  ax-in2 620  ax-bd0 16459  ax-bdim 16460  ax-bdn 16463  ax-bdeq 16466

This theorem depends on definitions:  df-bi 117  df-tru 1400

This theorem is referenced by: (None)