Theorem ancl 554

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		pm3.2 475	. 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓)))
2	1	a2i 15	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓)))

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:  exintr  1925  dfss2  3926  bnj1118  35404  bnj1128  35410  bnj1145  35413  bnj1174  35423