Theorem pm2.61 194

Description: Theorem *2.61 of [WhiteheadRussell] p. 107. Useful for eliminating an antecedent. (Contributed by NM, 4-Jan-1993.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)

Assertion

Ref	Expression
pm2.61	⊢ ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓))

Proof of Theorem pm2.61

Step	Hyp	Ref	Expression
1		pm2.6 193	. 2 ⊢ ((¬ 𝜑 → 𝜓) → ((𝜑 → 𝜓) → 𝜓))
2	1	com12 33	1 ⊢ ((𝜑 → 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  bnj1109  35417  jath  36490  bj-axseprep  37990  isltrn2N  41178  ltrnid  41193  ltrneq  41207  onfrALT  45532  onfrALTVD  45873