Theorem bdnthALT 16366

Description: Alternate proof of bdnth 16365 not using bdfal 16364. Then, bdfal 16364 can be proved from this theorem, using fal 1402. The total number of proof steps would be 17 (for bdnthALT 16366) + 3 = 20, which is more than 8 (for bdfal 16364) + 9 (for bdnth 16365) = 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 16363	. . 3 |- BOUNDED T.
2	1	ax-bdn 16348	. 2 |- BOUNDED -. T.
3		notnot 632	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1404	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 706	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 16355	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1396  BOUNDED wbd 16343

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 617  ax-in2 618  ax-bd0 16344  ax-bdim 16345  ax-bdn 16348  ax-bdeq 16351

This theorem depends on definitions:  df-bi 117  df-tru 1398

This theorem is referenced by: (None)