Theorem botel 36189

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 1556	. 2 ⊢ (⊥ → 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ⊥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 206  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)