Theorem 3anim1i 1152

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 22	. 2 ⊢ (𝜒 → 𝜒)
3		id 22	. 2 ⊢ (𝜃 → 𝜃)
4	1, 2, 3	3anim123i 1151	1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  syl3an1  1163  syl3anl1  1414  syl3anr1  1418  fnsuppres  8147  dif1en  9101  elfiun  9357  elioc2  13346  elico2  13347  elicc2  13348  dvdsleabs2  16258  subrngringnsg  20473  cphipval  25176  spthonpthon  29731  uhgrwkspth  29735  usgr2wlkspth  29739  upgriseupth  30186  cm2j  31599  bnj544  34877  btwnconn1lem4  36071  relowlssretop  37344  dalem53  39712  dalem54  39713  paddasslem14  39820  mzpcong  42954  itscnhlc0xyqsol  48747