Theorem falimd 1379

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 1378	. 2 ⊢ (⊥ → 𝜓)
2	1	adantl 277	1 ⊢ ((𝜑 ∧ ⊥) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 104  ⊥wfal 1369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  bj-axemptylem  15041