Theorem bdnthALT 15775

Description: Alternate proof of bdnth 15774 not using bdfal 15773. Then, bdfal 15773 can be proved from this theorem, using fal 1380. The total number of proof steps would be 17 (for bdnthALT 15775) + 3 = 20, which is more than 8 (for bdfal 15773) + 9 (for bdnth 15774) = 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 15772	. . 3 |- BOUNDED T.
2	1	ax-bdn 15757	. 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 15764	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1374  BOUNDED wbd 15752

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 15753  ax-bdim 15754  ax-bdn 15757  ax-bdeq 15760

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

This theorem is referenced by: (None)