Theorem jca2r 38790

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010.)

Hypotheses

Ref	Expression
jca2r.1	⊢ (𝜑 → (𝜓 → 𝜒))
jca2r.2	⊢ (𝜓 → 𝜃)

Assertion

Ref	Expression
jca2r	⊢ (𝜑 → (𝜓 → (𝜃 ∧ 𝜒)))

Proof of Theorem jca2r

Step	Hyp	Ref	Expression
1		jca2r.2	. . 3 ⊢ (𝜓 → 𝜃)
2	1	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
3		jca2r.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	jcad 512	1 ⊢ (𝜑 → (𝜓 → (𝜃 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  prter2  38816