Theorem pm2.61ian 765

Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005.)

Hypotheses

Ref	Expression
pm2.61ian.1	⊢ ((φ ∧ ψ) → χ)
pm2.61ian.2	⊢ ((¬ φ ∧ ψ) → χ)

Assertion

Ref	Expression
pm2.61ian	⊢ (ψ → χ)

Proof of Theorem pm2.61ian

Step	Hyp	Ref	Expression
1		pm2.61ian.1	. . 3 ⊢ ((φ ∧ ψ) → χ)
2	1	ex 423	. 2 ⊢ (φ → (ψ → χ))
3		pm2.61ian.2	. . 3 ⊢ ((¬ φ ∧ ψ) → χ)
4	3	ex 423	. 2 ⊢ (¬ φ → (ψ → χ))
5	2, 4	pm2.61i 156	1 ⊢ (ψ → χ)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  4cases  915  consensus  925  sbcom  2089  ax11indalem  2197  phi11lem1  4596  xpcan2  5059