Theorem simprld 530

Description: Deduction eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Hypothesis

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

Assertion

Ref	Expression
simprld	|- ( ph -> ch )

Proof of Theorem simprld

Step	Hyp	Ref	Expression
1		simprld.1	. . 3 |- ( ph -> ( ps /\ ( ch /\ th ) ) )
2	1	simprd 114	. 2 |- ( ph -> ( ch /\ th ) )
3	2	simpld 112	1 |- ( ph -> ch )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem is referenced by:  srglz  13541  lmodvsass  13869