Theorem bdnthALT 17083

Description: Alternate proof of bdnth 17082 not using bdfal 17081. Then, bdfal 17081 can be proved from this theorem, using fal 1409. The total number of proof steps would be 17 (for bdnthALT 17083) + 3 = 20, which is more than 8 (for bdfal 17081) + 9 (for bdnth 17082) = 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 17080	. . 3 |- BOUNDED T.
2	1	ax-bdn 17065	. 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 17072	1 |- BOUNDED ph

This proof depends on syntax axioms:   -. wn 3   T. wtru 1403  BOUNDED wbd 17060

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 17061  ax-bdim 17062  ax-bdn 17065  ax-bdeq 17068

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

This theorem is used by: (None)