Theorem axia1 2722

Description: Left 'and' elimination (intuitionistic logic axiom ax-ia1). (Contributed by Jim Kingdon, 21-May-2018.) (New usage is discouraged.)

Assertion

Ref	Expression
axia1	⊢ ((𝜑 ∧ 𝜓) → 𝜑)

Proof of Theorem axia1

Step	Hyp	Ref	Expression
1		simpl 488	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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-an 402

This theorem is used by: (None)