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  2086  barbari  2147  cesaro  2153  camestros  2154  calemos  2164  swopo  4341  elrnrexdm  5701  uchoice  6195  tfrcl  6422  ixpsnf1o  6795  fidcenumlemrk  7020  subhalfnqq  7481  enq0ref  7500  prarloc  7570  letrp1  8875  p1le  8876  peano2uz2  9433  uzind  9437  uzid  9615  qreccl  9716  fprodsplit1f  11799  lmodfopne  13882