Theorem ancri 324

Description: Deduction conjoining antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.)

Hypothesis

Ref	Expression
ancri.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
ancri	⊢ (𝜑 → (𝜓 ∧ 𝜑))

Proof of Theorem ancri

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

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:  bamalip  2147  gencbvex  2784  mosubt  2915  trsuc  4423  eusv2nf  4457  mosubopt  4692  issref  5012  fo00  5498  eqfnov2  5982  hashfzp1  10804  dfgcd2  12015