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  1848  mopick2  2163  ssrexf  3290  ssrexv  3293  ssdif  3344  ssrin  3434  reupick  3493  disjss1  4075  copsexg  4342  po3nr  4413  coss2  4892  fununi  5405  fiintim  7166  recexprlemlol  7889  recexprlemupu  7891  icoshft  10268  2ffzeq  10419  qbtwnxr  10561  ico0  10565  r19.2uz  11614  bezoutlemzz  12634  bezoutlemaz  12635  ptex  13408  rnglidlmmgm  14572  neiss  14941  uptx  15065  txcn  15066  bj-charfundcALT  16505