Theorem imim2 55

Description: A closed form of syllogism (see syl 14). Theorem *2.05 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 6-Sep-2012.)

Assertion

Ref	Expression
imim2	⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Proof of Theorem imim2

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2	1	imim2d 54	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  syldd  67  pm3.34  346  spimth  1735  spsbim  1843  bj-stim  14638  elabgft1  14670  bj-rspgt  14678  bj-findis  14871