Theorem jcad 519

Description: Deduction conjoining the consequents of two implications. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)

Hypotheses

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

Assertion

Ref	Expression
jcad	⊢ (φ → (ψ → (χ ∧ θ)))

Proof of Theorem jcad

Step	Hyp	Ref	Expression
1		jcad.1	. 2 ⊢ (φ → (ψ → χ))
2		jcad.2	. 2 ⊢ (φ → (ψ → θ))
3		pm3.2 434	. 2 ⊢ (χ → (θ → (χ ∧ θ)))
4	1, 2, 3	syl6c 60	1 ⊢ (φ → (ψ → (χ ∧ θ)))

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:  jctild  527  jctird  528  ancld  536  ancrd  537  anim12ii  553  oplem1  930  rr19.28v  2982  tfinltfinlem1  4501  iss  5001  funssres  5145  elpreima  5408  mapsn  6027  enadjlem1  6060  leltctr  6213  nchoicelem8  6297