Theorem ancri 317

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 300	1 ⊢ (𝜑 → (𝜓 ∧ 𝜑))

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106

This theorem is referenced by:  bamalip  2069  gencbvex  2665  mosubt  2792  trsuc  4249  eusv2nf  4278  mosubopt  4503  issref  4814  fo00  5289  eqfnov2  5752  hashfzp1  10228  dfgcd2  11277