Theorem import-P2.10a.SH 141

Description: Inference from import-P2.10a 140.

Hypothesis

Ref	Expression
import-P2.10a.SH.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
import-P2.10a.SH	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem import-P2.10a.SH

Step	Hyp	Ref	Expression
1		import-P2.10a.SH.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		import-P2.10a 140	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 ∧ 𝜓) → 𝜒))
3	1, 2	ax-MP 14	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wff-imp 10   ∧ wff-and 132

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133

This theorem is referenced by:  ndimp-P3.2  167