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  241  pm3.35  347  pm3.2im  638  jcn  653  pm2.65  661  annimim  688  condcOLD  856  pm2.26dc  909  ax10o  1738  issref  5065  fundif  5318  acexmidlem2  5941  findcard2  6986  findcard2s  6987  xpfi  7029  exmidontriim  7337  pcmptcl  12665  txlm  14751  bj-inf2vnlem1  15906  bj-findis  15915