Theorem pm3.35 278

Description: Conjunctive detachment. Theorem *3.35 of [WhiteheadRussell] p. 112.

Assertion

Ref	Expression
pm3.35	⊢ ((φ ∧ (φ → ψ)) → ψ)

Proof of Theorem pm3.35

Step	Hyp	Ref	Expression
1		pm2.27 30	. 2 ⊢ (φ → ((φ → ψ) → ψ))
2	1	imp 277	1 ⊢ ((φ ∧ (φ → ψ)) → ψ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  abai 366  ssiun 2018  aceq5 3563  ac5b 3574

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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