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  2163  gencbvex  2806  mosubt  2937  trsuc  4453  eusv2nf  4487  mosubopt  4724  issref  5048  fo00  5536  eqfnov2  6026  hashfzp1  10895  dfgcd2  12151