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  638  jcn  652  pm2.65  660  annimim  687  condcOLD  855  pm2.26dc  908  ax10o  1729  issref  5053  acexmidlem2  5922  findcard2  6959  findcard2s  6960  xpfi  7002  exmidontriim  7308  pcmptcl  12536  txlm  14599  bj-inf2vnlem1  15700  bj-findis  15709