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  8190  dif1en  9174  elfiun  9442  elioc2  13426  elico2  13427  elicc2  13428  dvdsleabs2  16331  subrngringnsg  20513  cphipval  25195  spthonpthon  29733  uhgrwkspth  29737  usgr2wlkspth  29741  upgriseupth  30188  cm2j  31601  bnj544  34925  btwnconn1lem4  36108  relowlssretop  37381  dalem53  39744  dalem54  39745  paddasslem14  39852  mzpcong  42996  itscnhlc0xyqsol  48745