Theorem anim12da 33506

Description: Conjoin antecedents and consequents in a deduction. (Contributed by Jeff Madsen, 16-Jun-2011.)

Hypotheses

Ref	Expression
anim12da.1	|- ( ( ph /\ ps ) -> th )
anim12da.2	|- ( ( ph /\ ch ) -> ta )

Assertion

Ref	Expression
anim12da	|- ( ( ph /\ ( ps /\ ch ) ) -> ( th /\ ta ) )

Proof of Theorem anim12da

Step	Hyp	Ref	Expression
1		anim12da.1	. 2 |- ( ( ph /\ ps ) -> th )
2		anim12da.2	. 2 |- ( ( ph /\ ch ) -> ta )
3	1, 2	anim12dan 882	1 |- ( ( ph /\ ( ps /\ ch ) ) -> ( th /\ ta ) )

Syntax hints:   -> wi 4   /\ wa 384

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

This theorem is referenced by:  ghomco  33690  rngohomco  33773  rngoisocnv  33780  rngoisoco  33781  idlsubcl  33822