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  3289  ssrexv  3292  ssdif  3342  ssrin  3432  reupick  3491  disjss1  4070  copsexg  4336  po3nr  4407  coss2  4886  fununi  5398  fiintim  7123  recexprlemlol  7846  recexprlemupu  7848  icoshft  10225  2ffzeq  10376  qbtwnxr  10518  ico0  10522  r19.2uz  11558  bezoutlemzz  12578  bezoutlemaz  12579  ptex  13352  rnglidlmmgm  14516  neiss  14880  uptx  15004  txcn  15005  bj-charfundcALT  16430