Theorem fal 1554

Description: The truth value ⊥ is refutable. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Mel L. O'Cat, 11-Mar-2012.)

Assertion

Ref	Expression
fal	⊢ ¬ ⊥

Proof of Theorem fal

Step	Hyp	Ref	Expression
1		tru 1544	. . 3 ⊢ ⊤
2	1	notnoti 143	. 2 ⊢ ¬ ¬ ⊤
3		df-fal 1553	. 2 ⊢ (⊥ ↔ ¬ ⊤)
4	2, 3	mtbir 323	1 ⊢ ¬ ⊥

Syntax hints:  ¬ wn 3  ⊤wtru 1541  ⊥wfal 1552

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-tru 1543  df-fal 1553

This theorem is referenced by:  nbfal  1555  bifal  1556  falim  1557  dfnot  1559  notfal  1568  falantru  1575  nffal  1805  alfal  1808  sbn1  2108  nonconne  2937  dfnul3  4300  noel  4301  vn0  4308  csbprc  4372  axnulALT  5259  axnul  5260  canthp1  10607  rlimno1  15620  1stccnp  23349  axsepg2ALT  35073  nexfal  36393  negsym1  36405  nandsym1  36410  bj-falor  36572  orfa  38076  fald  38123  dihglblem6  41334  ifpdfan  43455  ifpnot  43459  ifpid2  43460  ifpdfxor  43476