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Theorem reximi 2721

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 18-Oct-1996.)

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

**Assertion**
Ref	Expression
reximi	⊢ (∃x ∈ A φ → ∃x ∈ A ψ)

**Proof of Theorem reximi**
Step	Hyp	Ref	Expression
1		reximi.1	. . 3 ⊢ (φ → ψ)
2	1	a1i 10	. 2 ⊢ (x ∈ A → (φ → ψ))
3	2	reximia 2719	1 ⊢ (∃x ∈ A φ → ∃x ∈ A ψ)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∈ wcel 1710 ∃wrex 2615

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557

This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-ral 2619 df-rex 2620

This theorem is referenced by: r19.40 2762 reu3 3026 2reu5 3044 ssiun 4008 iinss 4017 lefinlteq 4463 sucevenodd 4510 sfinltfin 4535 vfinspsslem1 4550 pw1fin 6169 addlec 6208 nncdiv3 6277