Theorem bdnthALT 16156

Description: Alternate proof of bdnth 16155 not using bdfal 16154. Then, bdfal 16154 can be proved from this theorem, using fal 1402. The total number of proof steps would be 17 (for bdnthALT 16156) + 3 = 20, which is more than 8 (for bdfal 16154) + 9 (for bdnth 16155) = 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 16153	. . 3 |- BOUNDED T.
2	1	ax-bdn 16138	. 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 16145	1 |- BOUNDED ph

Syntax hints:   -. wn 3   T. wtru 1396  BOUNDED wbd 16133

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 16134  ax-bdim 16135  ax-bdn 16138  ax-bdeq 16141

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

This theorem is referenced by: (None)