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))

Syntax hints:   → wi 4   ∧ wa 358

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