Theorem ancl 318

Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994.)

Assertion

Ref	Expression
ancl	⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓)))

Proof of Theorem ancl

Step	Hyp	Ref	Expression
1		pm3.2 139	. 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓)))
2	1	a2i 11	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-2 7  ax-ia3 108

This theorem is used by:  equs4  1777  eupickbi  2169