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))

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-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  ccatval3  11381  ccatalpha  11395  ccatswrd  11456  pfxccatin12lem2  11517  pfxccat3  11520  pfxccat3a  11524  vfermltl  13050  powm2modprm  13051  modprmn0modprm0  13055  dvdsprmpweqle  13136  ixpsnbasval  14852  logbgcd1irr  16122  clwwlkccatlem  16760