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  2079  barbari  2140  cesaro  2146  camestros  2147  calemos  2157  swopo  4331  elrnrexdm  5685  tfrcl  6404  ixpsnf1o  6777  fidcenumlemrk  6999  subhalfnqq  7460  enq0ref  7479  prarloc  7549  letrp1  8853  p1le  8854  peano2uz2  9410  uzind  9414  uzid  9592  qreccl  9693  fprodsplit1f  11751  lmodfopne  13786