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  646  jcn  661  pm2.65  669  annimim  697  condcOLD  866  pm2.26dc  919  ax10o  1767  issref  5165  fundif  5420  acexmidlem2  6072  findcard2  7183  findcard2s  7184  xpfi  7229  exmidontriim  7571  pcmptcl  13099  txlm  15303  bj-inf2vnlem1  16910  bj-findis  16919