Theorem jctird 528

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

Hypotheses

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

Assertion

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

Proof of Theorem jctird

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

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:  anc2ri  541  fnun  5190  fco  5232