Theorem bdnthALT 15771

Description: Alternate proof of bdnth 15770 not using bdfal 15769. Then, bdfal 15769 can be proved from this theorem, using fal 1380. The total number of proof steps would be 17 (for bdnthALT 15771) + 3 = 20, which is more than 8 (for bdfal 15769) + 9 (for bdnth 15770) = 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 15768	. . 3 |- BOUNDED T.
2	1	ax-bdn 15753	. 2 |- BOUNDED -. T.
3		notnot 630	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1382	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 703	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 15760	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1374  BOUNDED wbd 15748

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 15749  ax-bdim 15750  ax-bdn 15753  ax-bdeq 15756

This theorem depends on definitions:  df-bi 117  df-tru 1376

This theorem is referenced by: (None)