Theorem pm3.34 765

Description: Theorem *3.34 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.34	⊢ (((𝜓 → 𝜒) ∧ (𝜑 → 𝜓)) → (𝜑 → 𝜒))

Proof of Theorem pm3.34

Step	Hyp	Ref	Expression
1		imim2 58	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2	1	imp 406	1 ⊢ (((𝜓 → 𝜒) ∧ (𝜑 → 𝜓)) → (𝜑 → 𝜒))

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by:  algcvgblem  16596  ax6e2ndeqALT  44908