Theorem mont 32408

Description: There does not exist at most one set, such that T. is true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
mont	|- -. E* x T.

Proof of Theorem mont

Step	Hyp	Ref	Expression
1		extt 32403	. . 3 |- E. x T.
2		unnt 32407	. . 3 |- -. E! x T.
3		mth8 158	. . 3 |- ( E. x T. -> ( -. E! x T. -> -. ( E. x T. -> E! x T. ) ) )
4	1, 2, 3	mp2 9	. 2 |- -. ( E. x T. -> E! x T. )
5		df-mo 2475	. 2 |- ( E* x T. <-> ( E. x T. -> E! x T. ) )
6	4, 5	mtbir 313	1 |- -. E* x T.

Syntax hints:   -. wn 3   -> wi 4   T. wtru 1484   E.wex 1704   E!weu 2470   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-nul 4789  ax-pow 4843

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by: (None)