Theorem pm2.43d 50

Description: Deduction absorbing redundant antecedent. (Contributed by NM, 18-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

Ref	Expression
pm2.43d.1	⊢ (𝜑 → (𝜓 → (𝜓 → 𝜒)))

Assertion

Ref	Expression
pm2.43d	⊢ (𝜑 → (𝜓 → 𝜒))

Proof of Theorem pm2.43d

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜓 → 𝜓)
2		pm2.43d.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜓 → 𝜒)))
3	1, 2	mpdi 43	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  loolin  102  pm2.18dc  856  sbcof2  1824  rgen2a  2551  rspct  2861  po2nr  4345  ordsuc  4600  funssres  5301  2elresin  5370  f1imass  5822  smoel  6359  tfri3  6426  nnmass  6546  sbthlem1  7024  genpcdl  7588  genpcuu  7589  recexprlemss1l  7704  recexprlemss1u  7705  grpid  13181  uniopn  14247  elabgft1  15434  bj-rspgt  15442