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)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  pm3.45  605  exdistrfor  1853  mopick2  2170  ssrexf  3310  ssrexv  3313  ssdif  3364  ssrin  3456  reupick  3517  disjss1  4112  copsexg  4384  po3nr  4455  coss2  4936  fununi  5449  fiintim  7238  recexprlemlol  7994  recexprlemupu  7996  icoshft  10403  2ffzeq  10559  qbtwnxr  10703  ico0  10707  r19.2uz  11774  bezoutlemzz  12797  bezoutlemaz  12798  ptex  13669  rnglidlmmgm  14884  neiss  15303  uptx  15427  txcn  15428  bj-charfundcALT  16957