Theorem anim1d 336

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.)

Hypothesis

Ref	Expression
anim1d.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
anim1d	⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜃)))

Proof of Theorem anim1d

Step	Hyp	Ref	Expression
1		anim1d.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		idd 21	. 2 ⊢ (𝜑 → (𝜃 → 𝜃))
3	1, 2	anim12d 335	1 ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → (𝜒 ∧ 𝜃)))

Syntax hints:   → wi 4   ∧ wa 104

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

This theorem is referenced by:  pm3.45  599  exdistrfor  1846  mopick2  2161  ssrexf  3286  ssrexv  3289  ssdif  3339  ssrin  3429  reupick  3488  disjss1  4065  copsexg  4331  po3nr  4402  coss2  4881  fununi  5392  fiintim  7109  recexprlemlol  7829  recexprlemupu  7831  icoshft  10203  2ffzeq  10354  qbtwnxr  10494  ico0  10498  r19.2uz  11525  bezoutlemzz  12544  bezoutlemaz  12545  ptex  13318  rnglidlmmgm  14481  neiss  14845  uptx  14969  txcn  14970  bj-charfundcALT  16281