Theorem ancli 323

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

Hypothesis

Ref	Expression
ancli.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
ancli	⊢ (𝜑 → (𝜑 ∧ 𝜓))

Proof of Theorem ancli

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝜑 → 𝜑)
2		ancli.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	jca 306	1 ⊢ (𝜑 → (𝜑 ∧ 𝜓))

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  2119  barbari  2180  cesaro  2186  camestros  2187  calemos  2197  swopo  4397  elrnrexdm  5774  uchoice  6283  tfrcl  6510  ixpsnf1o  6883  fidcenumlemrk  7121  subhalfnqq  7601  enq0ref  7620  prarloc  7690  letrp1  8995  p1le  8996  peano2uz2  9554  uzind  9558  uzid  9736  qreccl  9837  fprodsplit1f  12145  lmodfopne  14290