Theorem falimd 1311

Description: The truth value ⊥ implies anything. (Contributed by Mario Carneiro, 9-Feb-2017.)

Assertion

Ref	Expression
falimd	⊢ ((𝜑 ∧ ⊥) → 𝜓)

Proof of Theorem falimd

Step	Hyp	Ref	Expression
1		falim 1310	. 2 ⊢ (⊥ → 𝜓)
2	1	adantl 272	1 ⊢ ((𝜑 ∧ ⊥) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 103  ⊥wfal 1301

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 582  ax-in2 583

This theorem depends on definitions:  df-bi 116  df-tru 1299  df-fal 1302

This theorem is referenced by:  bj-axemptylem  12500