Theorem pm2.43 57

Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of [WhiteheadRussell] p. 106. (The proof was shortened by Mel L. O'Cat, 15-Aug-04.)

Assertion

Ref	Expression
pm2.43	⊢ ((φ → (φ → ψ)) → (φ → ψ))

Proof of Theorem pm2.43

Step	Hyp	Ref	Expression
1		pm2.27 30	. 2 ⊢ (φ → ((φ → ψ) → ψ))
2	1	a2i 8	1 ⊢ ((φ → (φ → ψ)) → (φ → ψ))

Syntax hints:   → wi 2

This theorem is referenced by:  pm2.43i 58  pm2.43d 59  pm5.4 146  rgen2 1248  trel 2048  relss 2480  tfrlem1 2949  suplem1pr 3955  suppsr2 4017  axsup 4088

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

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