Theorem jctild 527

Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005.)

Hypotheses

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

Assertion

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

Proof of Theorem jctild

Step	Hyp	Ref	Expression
1		jctild.2	. . 3 ⊢ (φ → θ)
2	1	a1d 22	. 2 ⊢ (φ → (ψ → θ))
3		jctild.1	. 2 ⊢ (φ → (ψ → χ))
4	2, 3	jcad 519	1 ⊢ (φ → (ψ → (θ ∧ χ)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  anc2li  540  ee12an  1363  ax12olem1  1927  2eu1  2284  xpcan  5058  xpcan2  5059