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  4288  noel  4289  vn0  4296  csbprc  4360  axnulALT  5243  axnul  5244  canthp1  10548  rlimno1  15561  1stccnp  23347  axsepg2ALT  35050  nexfal  36383  negsym1  36395  nandsym1  36400  bj-falor  36562  orfa  38066  fald  38113  dihglblem6  41323  ifpdfan  43443  ifpnot  43447  ifpid2  43448  ifpdfxor  43464