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Theorem wl-impchain-com-1.x 33591
Description: It is often convenient to have the antecedent under focus in first position, so we can apply immediate theorem forms (as opposed to deduction, tautology form). This series of theorems swaps the first with the last antecedent in an implication chain. This kind of swapping is self-inverse, whence we prefer it over, say, rotating theorems. A consequent can hide a tail of a longer chain, so theorems of this series appear as swapping a pair of antecedents with fixed offsets. This form of swapping antecedents is flexible enough to allow for any permutation of antecedents in an implication chain.

The first elements of this series correspond to com12 32, com13 88, com14 96 and com15 101 in the main part.

The proofs of this series aim at automated proving using a simple recursive scheme. It employs the previous theorem in the series along with a sample from the wl-impchain-mp-x 33587 series developed before. (Contributed by Wolf Lammen, 17-Nov-2019.)

Ref Expression

Proof of Theorem wl-impchain-com-1.x
StepHypRef Expression
1 tru 1642 1
Colors of variables: wff setvar class
Syntax hints:  wtru 1638
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 198  df-tru 1641
This theorem is referenced by: (None)
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