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Theorem anc2ri 580
Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)
Hypothesis
Ref Expression
anc2ri.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
anc2ri (𝜑 → (𝜓 → (𝜒𝜑)))

Proof of Theorem anc2ri
StepHypRef Expression
1 anc2ri.1 . 2 (𝜑 → (𝜓𝜒))
2 id 22 . 2 (𝜑𝜑)
31, 2jctird 566 1 (𝜑 → (𝜓 → (𝜒𝜑)))
Colors of variables: wff setvar class
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:  equvini  2345  fv3  6168  bropopvvv  7207  bropfvvvvlem  7208  issiga  29979  ontopbas  32104  bj-gl4lem  32256  clsk1independent  37861
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