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  4386  po3nr  4457  coss2  4938  fununi  5452  fiintim  7243  recexprlemlol  8000  recexprlemupu  8002  icoshft  10410  2ffzeq  10566  qbtwnxr  10710  ico0  10714  r19.2uz  11782  bezoutlemzz  12805  bezoutlemaz  12806  ptex  13678  rnglidlmmgm  14943  neiss  15388  uptx  15512  txcn  15513  bj-charfundcALT  17052