Theorem 2eximi 1577

Description: Inference adding two existential quantifiers to antecedent and consequent. (Contributed by NM, 3-Feb-2005.)

Hypothesis

Ref	Expression
eximi.1	⊢ (φ → ψ)

Assertion

Ref	Expression
2eximi	⊢ (∃x∃yφ → ∃x∃yψ)

Proof of Theorem 2eximi

Step	Hyp	Ref	Expression
1		eximi.1	. . 3 ⊢ (φ → ψ)
2	1	eximi 1576	. 2 ⊢ (∃yφ → ∃yψ)
3	2	eximi 1576	1 ⊢ (∃x∃yφ → ∃x∃yψ)

Syntax hints:   → wi 4  ∃wex 1541

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

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  excomimOLD  1858  2eu6  2289  cgsex2g  2892  cgsex4g  2893  vtocl2  2911  vtocl3  2912  mosubopt  4613  ssoprab2i  5581  ce0nnulb  6183