Theorem syl7bi 163

Description: A mixed syllogism inference from a doubly nested implication and a biconditional. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
syl7bi.1	|- ( ph <-> ps )
syl7bi.2	|- ( ch -> ( th -> ( ps -> ta ) ) )

Assertion

Ref	Expression
syl7bi	|- ( ch -> ( th -> ( ph -> ta ) ) )

Proof of Theorem syl7bi

Step	Hyp	Ref	Expression
1		syl7bi.1	. . 3 |- ( ph <-> ps )
2	1	biimpi 118	. 2 |- ( ph -> ps )
3		syl7bi.2	. 2 |- ( ch -> ( th -> ( ps -> ta ) ) )
4	2, 3	syl7 68	1 |- ( ch -> ( th -> ( ph -> ta ) ) )

Syntax hints:   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  necon1addc  2321  necon1ddc  2323  rspct  2694  2reuswapdc  2794  nn0lt2  8429  fzofzim  9197  ndvdssub  10330  bj-findis  10774