Theorem jcai 522

Description: Deduction replacing implication with conjunction. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
jcai.1	⊢ (φ → ψ)
jcai.2	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
jcai	⊢ (φ → (ψ ∧ χ))

Proof of Theorem jcai

Step	Hyp	Ref	Expression
1		jcai.1	. 2 ⊢ (φ → ψ)
2		jcai.2	. . 3 ⊢ (φ → (ψ → χ))
3	1, 2	mpd 14	. 2 ⊢ (φ → χ)
4	1, 3	jca 518	1 ⊢ (φ → (ψ ∧ χ))

Syntax hints:   → 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:  reu6  3025  opkthg  4131  f1o2d  5727  enprmaplem5  6080  nchoicelem17  6305