Theorem 19.22dvv 1294

Description: Deduction from Theorem 19.22 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.20dvv.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
19.22dvv	⊢ (φ → (∃x∃yψ → ∃x∃yχ))

Distinct variable groups:   φ,x   φ,y

Proof of Theorem 19.22dvv

Step	Hyp	Ref	Expression
1		19.20dvv.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	19.22dv 1292	. 2 ⊢ (φ → (∃yψ → ∃yχ))
3	2	19.22dv 1292	1 ⊢ (φ → (∃x∃yψ → ∃x∃yχ))

Syntax hints:   → wi 3  ∃wex 982

This theorem is referenced by:  cgsex2g 1835  cgsex4g 1836  cla42egv 1867  cla43egv 1869  relop 3281  th3q 4323

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

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