Theorem 3anim1i 1188

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)

Hypothesis

Ref	Expression
3animi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3anim1i	⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃))

Proof of Theorem 3anim1i

Step	Hyp	Ref	Expression
1		3animi.1	. 2 ⊢ (𝜑 → 𝜓)
2		id 19	. 2 ⊢ (𝜒 → 𝜒)
3		id 19	. 2 ⊢ (𝜃 → 𝜃)
4	1, 2, 3	3anim123i 1187	1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 981

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 983

This theorem is referenced by:  syl3an1  1283  syl3anl1  1298  syl3anr1  1302  elioc2  10078  elico2  10079  elicc2  10080  dvdsleabs2  12232  subrngringnsg  14042