Theorem imim1 15

Description: A closed form of syllogism (see syl 10). Theorem *2.06 of [WhiteheadRussell] p. 100.

Assertion

Ref	Expression
imim1	|- ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))

Proof of Theorem imim1

Step	Hyp	Ref	Expression
1		imim2 14	. 2 |- ((ps -> ch) -> ((ph -> ps) -> (ph -> ch)))
2	1	com12 11	1 |- ((ph -> ps) -> ((ps -> ch) -> (ph -> ch)))

Syntax hints:   -> wi 3

This theorem is referenced by:  imim1i 16  imim1d 28  pm2.83 31  looinv 83  pm3.33 357  immo 1415  sstr2 2067  intss 2549  suppsr2 5203  ivthlem3 7226

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7

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