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  8170  dif1en  9124  elfiun  9381  elioc2  13370  elico2  13371  elicc2  13372  dvdsleabs2  16282  subrngringnsg  20462  cphipval  25143  spthonpthon  29681  uhgrwkspth  29685  usgr2wlkspth  29689  upgriseupth  30136  cm2j  31549  bnj544  34884  btwnconn1lem4  36078  relowlssretop  37351  dalem53  39719  dalem54  39720  paddasslem14  39827  mzpcong  42961  itscnhlc0xyqsol  48754