Theorem ndimi-P3.5 170

Description: Natural Deduction: '→' Introduction Rule.

If we can deduce '𝜓' after assuming '𝜑', then we can conclude '𝜑 → 𝜓' with '𝜑' discharged.

Hypothesis

Ref	Expression
ndimi-P3.5.1	⊢ ((𝛾 ∧ 𝜑) → 𝜓)

Assertion

Ref	Expression
ndimi-P3.5	⊢ (𝛾 → (𝜑 → 𝜓))

Proof of Theorem ndimi-P3.5

Step	Hyp	Ref	Expression
1		ndimi-P3.5.1	. 2 ⊢ ((𝛾 ∧ 𝜑) → 𝜓)
2	1	export-P2.10b.SH 143	1 ⊢ (𝛾 → (𝜑 → 𝜓))

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:  ndfalsei-P3.19  184  rcp-NDASM1of1  192  rcp-NDIMP0addall  207  rcp-NDIMI2  224  rcp-NDIMI3  225  rcp-NDIMI4  226  rcp-NDIMI5  227