Theorem falimd 1258

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 1257	. 2 ⊢ (⊥ → 𝜓)
2	1	adantl 262	1 ⊢ ((𝜑 ∧ ⊥) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 97  ⊥wfal 1248

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  bj-axemptylem  10012