Theorem jccil 563

Description: Inference conjoining a consequent of a consequent to the left of the consequent in an implication. Remark: One can also prove this theorem using syl 17 and jca 554 (as done in jccir 562), which would be 4 bytes shorter, but one step longer than the current proof. (Proof modification is discouraged.) (Contributed by AV, 20-Aug-2019.)

Hypotheses

Ref	Expression
jccir.1	|- ( ph -> ps )
jccir.2	|- ( ps -> ch )

Assertion

Ref	Expression
jccil	|- ( ph -> ( ch /\ ps ) )

Proof of Theorem jccil

Step	Hyp	Ref	Expression
1		jccir.1	. . 3 |- ( ph -> ps )
2		jccir.2	. . 3 |- ( ps -> ch )
3	1, 2	jccir 562	. 2 |- ( ph -> ( ps /\ ch ) )
4	3	ancomd 467	1 |- ( ph -> ( ch /\ ps ) )

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:  inatsk  9600  relexpindlem  13803