Theorem bdnthALT 16731

Description: Alternate proof of bdnth 16730 not using bdfal 16729. Then, bdfal 16729 can be proved from this theorem, using fal 1405. The total number of proof steps would be 17 (for bdnthALT 16731) + 3 = 20, which is more than 8 (for bdfal 16729) + 9 (for bdnth 16730) = 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 16728	. . 3 |- BOUNDED T.
2	1	ax-bdn 16713	. 2 |- BOUNDED -. T.
3		notnot 634	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1407	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 709	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 16720	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1399  BOUNDED wbd 16708

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 16709  ax-bdim 16710  ax-bdn 16713  ax-bdeq 16716

This theorem depends on definitions:  df-bi 117  df-tru 1401

This theorem is referenced by: (None)