Theorem jctird 300

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 291	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃)))

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101

This theorem is referenced by:  anc2ri  313  ordunisuc2r  4240  fnun  5005  fco  5056  cauappcvgprlemladdru  6754  cauappcvgprlemladdrl  6755  caucvgprlemnkj  6764