Theorem botel 38781

Description: An inference for bottom elimination. (Contributed by Giovanni Mascellani, 24-May-2019.)

Hypothesis

Ref	Expression
botel.1	⊢ (𝜑 → ⊥)

Assertion

Ref	Expression
botel	⊢ (𝜑 → 𝜓)

Proof of Theorem botel

Step	Hyp	Ref	Expression
1		botel.1	. 2 ⊢ (𝜑 → ⊥)
2		falim 1587	. 2 ⊢ (⊥ → 𝜓)
3	1, 2	syl 18	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4  ⊥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-tru 1573  df-fal 1583

This theorem is used by: (None)