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  2945  dfnul3  4317  noel  4318  vn0  4325  csbprc  4389  axnulALT  5279  axnul  5280  canthp1  10673  rlimno1  15675  1stccnp  23405  axsepg2ALT  35119  nexfal  36428  negsym1  36440  nandsym1  36445  bj-falor  36607  orfa  38111  fald  38158  dihglblem6  41364  ifpdfan  43457  ifpnot  43461  ifpid2  43462  ifpdfxor  43478