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  3246  ssrexv  3249  ssdif  3299  ssrin  3389  reupick  3448  disjss1  4017  copsexg  4278  po3nr  4346  coss2  4823  fununi  5327  fiintim  7001  recexprlemlol  7710  recexprlemupu  7712  icoshft  10082  2ffzeq  10233  qbtwnxr  10364  ico0  10368  r19.2uz  11175  bezoutlemzz  12194  bezoutlemaz  12195  ptex  12966  rnglidlmmgm  14128  neiss  14470  uptx  14594  txcn  14595  bj-charfundcALT  15539