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Theorem syl7ib 216
Description: A mixed syllogism inference from a doubly nested implication and a biconditional.
Hypotheses
Ref Expression
syl7ib.1 |- (ph -> (ps -> (ch -> th)))
syl7ib.2 |- (ta <-> ch)
Assertion
Ref Expression
syl7ib |- (ph -> (ps -> (ta -> th)))
Proof of Theorem syl7ib
StepHypRef Expression
1 syl7ib.1 . 2 |- (ph -> (ps -> (ch -> th)))
2 syl7ib.2 . . 3 |- (ta <-> ch)
32biimp 151 . 2 |- (ta -> ch)
41, 3syl7 23 1 |- (ph -> (ps -> (ta -> th)))
Colors of variables: wff set class
Syntax hints:   -> wi 3   <-> wb 146
This theorem is referenced by:  jao 340  zfpair 2767  subtop 7588  uninqs 10342
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7
This theorem depends on definitions:  df-bi 147
Copyright terms: Public domain