Theorem jctird 317

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 307	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  anc2ri  330  ordunisuc2r  4661  fnun  5489  fco  5552  fcof  5894  fiintim  7238  cauappcvgprlemladdru  8024  cauappcvgprlemladdrl  8025  caucvgprlemnkj  8034  dvdsdivcl  12636  cnrest2  15428  cnptopresti  15430  bdxmet  15693  lgsdir  16320