Theorem bi2.04 141

Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of [WhiteheadRussell] p. 122.

Assertion

Ref	Expression
bi2.04	⊢ ((φ → (ψ → χ)) ↔ (ψ → (φ → χ)))

Proof of Theorem bi2.04

Step	Hyp	Ref	Expression
1		pm2.04 31	. 2 ⊢ ((φ → (ψ → χ)) → (ψ → (φ → χ)))
2		pm2.04 31	. 2 ⊢ ((ψ → (φ → χ)) → (φ → (ψ → χ)))
3	1, 2	impbi 139	1 ⊢ ((φ → (ψ → χ)) ↔ (ψ → (φ → χ)))

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  or12 217  sbcom 916  sbcom2 992  mo 1020  r19.21v 1260  rax5 1472  unissb 1941  aceq1 3552  kmlem4 3583  chcmh 5148  elat2 5739

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

This theorem depends on definitions:  df-bi 128

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