Theorem pm2.43b 52

Description: Inference absorbing redundant antecedent. (Contributed by NM, 31-Oct-1995.)

Hypothesis

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

Assertion

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

Proof of Theorem pm2.43b

Step	Hyp	Ref	Expression
1		pm2.43b.1	. . 3 ⊢ (𝜓 → (𝜑 → (𝜓 → 𝜒)))
2	1	pm2.43a 51	. 2 ⊢ (𝜓 → (𝜑 → 𝜒))
3	2	com12 30	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:  trel  4087  trss  4089  elirr  4518  en2lp  4531  funfvima  5716  nnmulcl  8878  ico0  10197  ioc0  10198  bj-nn0sucALT  13860