Theorem ancli 323

Description: Deduction conjoining antecedent to left of consequent. (Contributed by NM, 12-Aug-1993.)

Hypothesis

Ref	Expression
ancli.1	|- ( ph -> ps )

Assertion

Ref	Expression
ancli	|- ( ph -> ( ph /\ ps ) )

Proof of Theorem ancli

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ph -> ph )
2		ancli.1	. 2 |- ( ph -> ps )
3	1, 2	jca 306	1 |- ( ph -> ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  pm4.45im  334  mo23  2121  barbari  2182  cesaro  2188  camestros  2189  calemos  2199  swopo  4409  elrnrexdm  5794  uchoice  6309  tfrcl  6573  ixpsnf1o  6948  fidcenumlemrk  7196  subhalfnqq  7677  enq0ref  7696  prarloc  7766  letrp1  9070  p1le  9071  peano2uz2  9631  uzind  9635  uzid  9814  qreccl  9920  fprodsplit1f  12258  lmodfopne  14405  wlkres  16303