Theorem falimd 1557

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 1556	. 2 ⊢ (⊥ → 𝜓)
2	1	adantl 481	1 ⊢ ((𝜑 ∧ ⊥) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ⊥wfal 1551

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 207  df-an 396  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)