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  601  exdistrfor  1849  mopick2  2164  ssrexf  3299  ssrexv  3302  ssdif  3353  ssrin  3445  reupick  3504  disjss1  4090  copsexg  4359  po3nr  4430  coss2  4910  fununi  5423  fiintim  7190  recexprlemlol  7940  recexprlemupu  7942  icoshft  10322  2ffzeq  10474  qbtwnxr  10616  ico0  10620  r19.2uz  11674  bezoutlemzz  12694  bezoutlemaz  12695  ptex  13469  rnglidlmmgm  14636  neiss  15007  uptx  15131  txcn  15132  bj-charfundcALT  16571