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  599  exdistrfor  1846  mopick2  2161  ssrexf  3286  ssrexv  3289  ssdif  3339  ssrin  3429  reupick  3488  disjss1  4065  copsexg  4330  po3nr  4401  coss2  4878  fununi  5389  fiintim  7101  recexprlemlol  7821  recexprlemupu  7823  icoshft  10194  2ffzeq  10345  qbtwnxr  10485  ico0  10489  r19.2uz  11512  bezoutlemzz  12531  bezoutlemaz  12532  ptex  13305  rnglidlmmgm  14468  neiss  14832  uptx  14956  txcn  14957  bj-charfundcALT  16196