Theorem bdnthALT 15970

Description: Alternate proof of bdnth 15969 not using bdfal 15968. Then, bdfal 15968 can be proved from this theorem, using fal 1380. The total number of proof steps would be 17 (for bdnthALT 15970) + 3 = 20, which is more than 8 (for bdfal 15968) + 9 (for bdnth 15969) = 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 15967	. . 3 |- BOUNDED T.
2	1	ax-bdn 15952	. 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 15959	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1374  BOUNDED wbd 15947

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 15948  ax-bdim 15949  ax-bdn 15952  ax-bdeq 15955

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

This theorem is referenced by: (None)