Theorem falimd 1588

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 1587	. 2 ⊢ (⊥ → 𝜓)
2	1	adantl 487	1 ⊢ ((𝜑 ∧ ⊥) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583

This theorem is used by: (None)