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  4324  elrnrexdm  5676  tfrcl  6389  ixpsnf1o  6762  fidcenumlemrk  6983  subhalfnqq  7443  enq0ref  7462  prarloc  7532  letrp1  8835  p1le  8836  peano2uz2  9390  uzind  9394  uzid  9572  qreccl  9672  fprodsplit1f  11674  lmodfopne  13642