Theorem jccir 530

Description: Inference conjoining a consequent of a consequent to the right of the consequent in an implication. See also ex-natded5.3i 30760. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by AV, 20-Aug-2019.)

Hypotheses

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

Assertion

Ref	Expression
jccir	⊢ (𝜑 → (𝜓 ∧ 𝜒))

Proof of Theorem jccir

Step	Hyp	Ref	Expression
1		jccir.1	. 2 ⊢ (𝜑 → 𝜓)
2		jccir.2	. . 3 ⊢ (𝜓 → 𝜒)
3	1, 2	syl 18	. 2 ⊢ (𝜑 → 𝜒)
4	1, 3	jca 520	1 ⊢ (𝜑 → (𝜓 ∧ 𝜒))

Syntax hints:   → wi 4   ∧ wa 400

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 210  df-an 401

This theorem is referenced by:  jccil  531  oelim2  8577  maxprmfct  16763  chpmat1dlem  22992  chpdmatlem2  22996  leordtvallem1  23367  leordtvallem2  23368  mbfmax  25808  wlklnwwlkln2lem  30231  0wlkonlem1  30469  2cycl2d  35631  relowlpssretop  38010  ntrclsk13  44797  smonoord  48114