Theorem pm2.27 40

Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens ax-mp 5. Theorem *2.27 of [WhiteheadRussell] p. 104. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem pm2.27

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	com12 30	1 |- ( ph -> ( ( ph -> ps ) -> ps ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  pm2.43  53  com23  78  biimt  240  pm3.35  345  pm3.2im  627  jcn  641  pm2.65  649  annimim  676  condcOLD  840  pm2.26dc  893  ax10o  1694  issref  4929  acexmidlem2  5779  findcard2  6791  findcard2s  6792  xpfi  6826  txlm  12487  bj-inf2vnlem1  13339  bj-findis  13348