Theorem falimd 1555

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 1554	. 2 ⊢ (⊥ → 𝜓)
2	1	adantl 484	1 ⊢ ((𝜑 ∧ ⊥) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 398  ⊥wfal 1549

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 209  df-an 399  df-tru 1540  df-fal 1550

This theorem is referenced by: (None)