Theorem bdnthALT 16253

Description: Alternate proof of bdnth 16252 not using bdfal 16251. Then, bdfal 16251 can be proved from this theorem, using fal 1402. The total number of proof steps would be 17 (for bdnthALT 16253) + 3 = 20, which is more than 8 (for bdfal 16251) + 9 (for bdnth 16252) = 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 16250	. . 3 |- BOUNDED T.
2	1	ax-bdn 16235	. 2 |- BOUNDED -. T.
3		notnot 632	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1404	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 706	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 16242	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1396  BOUNDED wbd 16230

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 617  ax-in2 618  ax-bd0 16231  ax-bdim 16232  ax-bdn 16235  ax-bdeq 16238

This theorem depends on definitions:  df-bi 117  df-tru 1398

This theorem is referenced by: (None)