Theorem jca2 556

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 12-Oct-2010.)

Hypotheses

Ref	Expression
jca2.1	⊢ (𝜑 → (𝜓 → 𝜒))
jca2.2	⊢ (𝜓 → 𝜃)

Assertion

Ref	Expression
jca2	⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃)))

Proof of Theorem jca2

Step	Hyp	Ref	Expression
1		jca2.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		jca2.2	. . 3 ⊢ (𝜓 → 𝜃)
3	2	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
4	1, 3	jcad 555	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃)))

Syntax hints:   → wi 4   ∧ wa 384

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 197  df-an 386

This theorem is referenced by:  cvmlift2lem10  31294  relcnveq3  34092  iss2  34112  jca3  34140