Theorem bdnthALT 16861

Description: Alternate proof of bdnth 16860 not using bdfal 16859. Then, bdfal 16859 can be proved from this theorem, using fal 1409. The total number of proof steps would be 17 (for bdnthALT 16861) + 3 = 20, which is more than 8 (for bdfal 16859) + 9 (for bdnth 16860) = 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 16858	. . 3 |- BOUNDED T.
2	1	ax-bdn 16843	. 2 |- BOUNDED -. T.
3		notnot 638	. . . 4 |- ( T. -> -. -. T. )
4	3	mptru 1411	. . 3 |- -. -. T.
5		bdnth.1	. . 3 |- -. ph
6	4, 5	2false 713	. 2 |- ( -. T. <-> ph )
7	2, 6	bd0 16850	1 |- BOUNDED ph

This proof depends on syntax axioms:   -. wn 3   T. wtru 1403  BOUNDED wbd 16838

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-bd0 16839  ax-bdim 16840  ax-bdn 16843  ax-bdeq 16846

This proof depends on definitions:  df-bi 117  df-tru 1405

This theorem is used by: (None)