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  8121  dif1en  9071  elfiun  9314  elioc2  13309  elico2  13310  elicc2  13311  dvdsleabs2  16223  subrngringnsg  20468  cphipval  25170  spthonpthon  29729  uhgrwkspth  29733  usgr2wlkspth  29737  upgriseupth  30187  cm2j  31600  bnj544  34906  btwnconn1lem4  36134  relowlssretop  37407  dalem53  39834  dalem54  39835  paddasslem14  39942  mzpcong  43075  itscnhlc0xyqsol  48876