Theorem jccir 521

Description: Inference conjoining a consequent of a consequent to the right of the consequent in an implication. See also ex-natded5.3i 30232. (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 17	. 2 ⊢ (𝜑 → 𝜒)
4	1, 3	jca 511	1 ⊢ (𝜑 → (𝜓 ∧ 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 206  df-an 396

This theorem is referenced by:  jccil  522  oelim2  8616  maxprmfct  16680  chpmat1dlem  22750  chpdmatlem2  22754  leordtvallem1  23127  leordtvallem2  23128  mbfmax  25591  wlklnwwlkln2lem  29706  0wlkonlem1  29941  2cycl2d  34749  relowlpssretop  36843  ntrclsk13  43501  smonoord  46711