Theorem pm2.27 30

Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens. Theorem *2.27 of [WhiteheadRussell] p. 104.

Assertion

Ref	Expression
pm2.27	|- (ph -> ((ph -> ps) -> ps))

Proof of Theorem pm2.27

Step	Hyp	Ref	Expression
1		id 9	. 2 |- ((ph -> ps) -> (ph -> ps))
2	1	com12 13	1 |- (ph -> ((ph -> ps) -> ps))

Syntax hints:   -> wi 2

This theorem is referenced by:  pm2.43 57  pm3.2im 107  mth8 108  ja 118  a1bi 172  pm3.35 278  biimt 549  meredith 644  r19.27av 1293  tfindsg 2402

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

metamath.org