Theorem anim1ci 341

Description: Introduce conjunct to both sides of an implication. (Contributed by Peter Mazsa, 24-Sep-2022.)

Hypothesis

Ref	Expression
anim1i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
anim1ci	⊢ ((𝜑 ∧ 𝜒) → (𝜒 ∧ 𝜓))

Proof of Theorem anim1ci

Step	Hyp	Ref	Expression
1		anim1i.1	. 2 ⊢ (𝜑 → 𝜓)
2		id 19	. 2 ⊢ (𝜒 → 𝜒)
3	1, 2	anim12ci 339	1 ⊢ ((𝜑 ∧ 𝜒) → (𝜒 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  ccatval3  11177  ccatalpha  11191  ccatswrd  11252  pfxccatin12lem2  11313  pfxccat3  11316  pfxccat3a  11320  vfermltl  12826  powm2modprm  12827  modprmn0modprm0  12831  dvdsprmpweqle  12912  ixpsnbasval  14483  logbgcd1irr  15694  clwwlkccatlem  16254