Theorem pm2.43a 50

Description: Inference absorbing redundant antecedent. (Contributed by NM, 7-Nov-1995.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

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

Assertion

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

Proof of Theorem pm2.43a

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜓 → 𝜓)
2		pm2.43a.1	. 2 ⊢ (𝜓 → (𝜑 → (𝜓 → 𝜒)))
3	1, 2	mpid 41	1 ⊢ (𝜓 → (𝜑 → 𝜒))

Syntax hints:   → wi 4

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

This theorem is referenced by:  pm2.43b  51  rspc  2695  rspc2gv  2712  intss1  3651  fvopab3ig  5267  nndi  6088  uzind2  8459  ssfzo12  9233