Theorem export-P2.10b.SH 143

Description: Inference from export-P2.10b 142.

Hypothesis

Ref	Expression
export-P2.10b.SH.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
export-P2.10b.SH	⊢ (𝜑 → (𝜓 → 𝜒))

Proof of Theorem export-P2.10b.SH

Step	Hyp	Ref	Expression
1		export-P2.10b.SH.1	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2		export-P2.10b 142	. 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:  orelim-P2.11c  150  ndnegi-P3.3  168  ndimi-P3.5  170  ndore-P3.12  177