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	⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))

Proof of Theorem pm2.27

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2	1	com12 30	1 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))

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  640  jcn  655  pm2.65  663  annimim  690  condcOLD  859  pm2.26dc  912  ax10o  1761  issref  5114  fundif  5368  acexmidlem2  6007  findcard2  7064  findcard2s  7065  xpfi  7110  exmidontriim  7423  pcmptcl  12886  txlm  14974  bj-inf2vnlem1  16442  bj-findis  16451