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Theorem ancld 536
Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)
Hypothesis
Ref Expression
ancld.1 (φ → (ψχ))
Assertion
Ref Expression
ancld (φ → (ψ → (ψ χ)))

Proof of Theorem ancld
StepHypRef Expression
1 idd 21 . 2 (φ → (ψψ))
2 ancld.1 . 2 (φ → (ψχ))
31, 2jcad 519 1 (φ → (ψ → (ψ χ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  mopick2  2271  cgsexg  2890  cgsex2g  2891  cgsex4g  2892  reximdva0  3561  difsn  3845  preq12b  4127  nnpw1ex  4484  tfin11  4493  vinf  4555  dmcosseq  4973  ssreseq  4997  fnoprabg  5585  dmfrec  6316
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