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))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  trel  4236  trss  4238  elirr  4688  en2lp  4701  funfvima  5950  mapfset  6945  nnmulcl  9326  ico0  10698  ioc0  10699  bj-nn0sucALT  17016