Theorem ancri 322

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 304	1 ⊢ (𝜑 → (𝜓 ∧ 𝜑))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107

This theorem is referenced by:  bamalip  2135  gencbvex  2772  mosubt  2903  trsuc  4400  eusv2nf  4434  mosubopt  4669  issref  4986  fo00  5468  eqfnov2  5949  hashfzp1  10737  dfgcd2  11947