Theorem 3impcombi 39044

Description: A 1-hypothesis propositional calculus deduction. (Contributed by Alan Sare, 25-Sep-2017.)

Hypothesis

Ref	Expression
3impcombi.1	|- ( ( ph /\ ps /\ ph ) -> ( ch <-> th ) )

Assertion

Ref	Expression
3impcombi	|- ( ( ps /\ ph /\ ch ) -> th )

Proof of Theorem 3impcombi

Step	Hyp	Ref	Expression
1		3impcombi.1	. . . . 5 |- ( ( ph /\ ps /\ ph ) -> ( ch <-> th ) )
2	1	biimpd 219	. . . 4 |- ( ( ph /\ ps /\ ph ) -> ( ch -> th ) )
3	2	3anidm13 1384	. . 3 |- ( ( ph /\ ps ) -> ( ch -> th ) )
4	3	ancoms 469	. 2 |- ( ( ps /\ ph ) -> ( ch -> th ) )
5	4	3impia 1261	1 |- ( ( ps /\ ph /\ ch ) -> th )

Syntax hints:   -> wi 4   <-> wb 196   /\ w3a 1037

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 197  df-an 386  df-3an 1039

This theorem is referenced by:  isosctrlem1ALT  39170