Theorem 3anbi3i 828

Description: Inference adding two conjuncts to each side of a biconditional.

Hypothesis

Ref	Expression
3anbi1i.1	⊢ (φ ↔ ψ)

Assertion

Ref	Expression
3anbi3i	⊢ ((χ ⋀ θ ⋀ φ) ↔ (χ ⋀ θ ⋀ ψ))

Proof of Theorem 3anbi3i

Step	Hyp	Ref	Expression
1		pm4.2 170	. 2 ⊢ (χ ↔ χ)
2		pm4.2 170	. 2 ⊢ (θ ↔ θ)
3		3anbi1i.1	. 2 ⊢ (φ ↔ ψ)
4	1, 2, 3	3anbi123i 824	1 ⊢ ((χ ⋀ θ ⋀ φ) ↔ (χ ⋀ θ ⋀ ψ))

Syntax hints:   ↔ wb 146   ⋀ w3a 777

This theorem is referenced by:  efcn 7423  lmbr2 7926  axgroth2 8773

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 779

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