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Theorem anim1i 551

Description: Introduce conjunct to both sides of an implication. (Contributed by NM, 5-Aug-1993.)

**Hypothesis**
Ref	Expression
anim1i.1	⊢ (φ → ψ)

**Assertion**
Ref	Expression
anim1i	⊢ ((φ ∧ χ) → (ψ ∧ χ))

**Proof of Theorem anim1i**
Step	Hyp	Ref	Expression
1		anim1i.1	. 2 ⊢ (φ → ψ)
2		id 19	. 2 ⊢ (χ → χ)
3	1, 2	anim12i 549	1 ⊢ ((φ ∧ χ) → (ψ ∧ χ))

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360

This theorem is referenced by: sylanl1 631 sylanr1 633 disamis 2314 sucevenodd 4510 sucoddeven 4511 fun11uni 5162 fores 5278 isomin 5496 ndmovass 5618