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  2086  barbari  2147  cesaro  2153  camestros  2154  calemos  2164  swopo  4342  elrnrexdm  5704  uchoice  6204  tfrcl  6431  ixpsnf1o  6804  fidcenumlemrk  7029  subhalfnqq  7500  enq0ref  7519  prarloc  7589  letrp1  8894  p1le  8895  peano2uz2  9452  uzind  9456  uzid  9634  qreccl  9735  fprodsplit1f  11818  lmodfopne  13960