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

Step	Hyp	Ref	Expression
1		syl7ib.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		syl7ib.2	. . 3 |- (ta <-> ch)
3	2	biimp 151	. 2 |- (ta -> ch)
4	1, 3	syl7 23	1 |- (ph -> (ps -> (ta -> th)))

Syntax hints:   -> wi 3   <-> wb 146

This theorem is referenced by:  jao 340  zfpair 2773  subtop 7606  uninqs 10400

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