Theorem pm2.27 39

Description: This theorem, called "Assertion," can be thought of as closed form of modus ponens ax-mp 7. 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-1 5  ax-2 6  ax-mp 7

This theorem is referenced by:  pm2.43  52  com23  77  biimt  239  pm3.35  339  pm3.2im  598  mth8  611  pm2.65  617  condc  782  annimim  815  pm2.26dc  846  ax10o  1643  issref  4727  acexmidlem2  5529  findcard2  6373  findcard2s  6374  bj-inf2vnlem1  10765  bj-findis  10774