Theorem syldbl2 1333

Description: Stacked hypotheseis implies goal. (Contributed by Stanislas Polu, 9-Mar-2020.)

Hypothesis

Ref	Expression
syldbl2.1	|- ( ( ph /\ ps ) -> ( ps -> th ) )

Assertion

Ref	Expression
syldbl2	|- ( ( ph /\ ps ) -> th )

Proof of Theorem syldbl2

Step	Hyp	Ref	Expression
1		syldbl2.1	. . 3 |- ( ( ph /\ ps ) -> ( ps -> th ) )
2	1	com12 30	. 2 |- ( ps -> ( ( ph /\ ps ) -> th ) )
3	2	anabsi7 587	1 |- ( ( ph /\ ps ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  reldmm  5000  elfzoextl  10609