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  597  exdistrfor  1814  mopick2  2128  ssrexf  3245  ssrexv  3248  ssdif  3298  ssrin  3388  reupick  3447  disjss1  4016  copsexg  4277  po3nr  4345  coss2  4822  fununi  5326  fiintim  6992  recexprlemlol  7693  recexprlemupu  7695  icoshft  10065  2ffzeq  10216  qbtwnxr  10347  ico0  10351  r19.2uz  11158  bezoutlemzz  12169  bezoutlemaz  12170  ptex  12935  rnglidlmmgm  14052  neiss  14386  uptx  14510  txcn  14511  bj-charfundcALT  15455