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))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is used by:  bamalip  2208  gencbvex  2869  mosubt  3003  trsuc  4567  eusv2nf  4602  mosubopt  4840  issref  5170  fo00  5677  eqfnov2  6196  hashfzp1  11265  dfgcd2  12791