Theorem falim 1328

Description: ⊥ implies anything. (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.)

Assertion

Ref	Expression
falim	⊢ ( ⊥ → φ)

Proof of Theorem falim

Step	Hyp	Ref	Expression
1		fal 1322	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 123	1 ⊢ ( ⊥ → φ)

Syntax hints:   → wi 4   ⊥ wfal 1317

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 177  df-tru 1319  df-fal 1320

This theorem is referenced by:  falimd  1329  dfnot  1332  falimtru  1346  tbw-bijust  1463  tbw-negdf  1464  tbw-ax4  1468  merco1  1478  merco2  1501