Theorem bdnthALT 15397

Description: Alternate proof of bdnth 15396 not using bdfal 15395. Then, bdfal 15395 can be proved from this theorem, using fal 1371. The total number of proof steps would be 17 (for bdnthALT 15397) + 3 = 20, which is more than 8 (for bdfal 15395) + 9 (for bdnth 15396) = 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 15394	. . 3 |- BOUNDED T.
2	1	ax-bdn 15379	. 2 |- BOUNDED -. T.
3		notnot 630	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1373	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 702	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 15386	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1365  BOUNDED wbd 15374

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 15375  ax-bdim 15376  ax-bdn 15379  ax-bdeq 15382

This theorem depends on definitions:  df-bi 117  df-tru 1367

This theorem is referenced by: (None)