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  642  jcn  657  pm2.65  665  annimim  693  condcOLD  862  pm2.26dc  915  ax10o  1763  issref  5144  fundif  5399  acexmidlem2  6046  findcard2  7145  findcard2s  7146  xpfi  7191  exmidontriim  7531  pcmptcl  13036  txlm  15136  bj-inf2vnlem1  16732  bj-findis  16741