Theorem anc2li 329

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)

Hypothesis

Ref	Expression
anc2li.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
anc2li	⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒)))

Proof of Theorem anc2li

Step	Hyp	Ref	Expression
1		anc2li.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		id 19	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	jctild 316	1 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒)))

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

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  imdistani  449  equvini  1811  sssnm  3879  tfis  4730  indpi  7710  ballotfilemfc0  13284  ballotfilemfcc  13285