xchbinxr - New Foundations Explorer

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Theorem xchbinxr 302

Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)

**Hypotheses**
Ref	Expression
xchbinxr.1	⊢ (φ ↔ ¬ ψ)
xchbinxr.2	⊢ (χ ↔ ψ)

**Assertion**
Ref	Expression
xchbinxr	⊢ (φ ↔ ¬ χ)

**Proof of Theorem xchbinxr**
Step	Hyp	Ref	Expression
1		xchbinxr.1	. 2 ⊢ (φ ↔ ¬ ψ)
2		xchbinxr.2	. . 3 ⊢ (χ ↔ ψ)
3	2	bicomi 193	. 2 ⊢ (ψ ↔ χ)
4	1, 3	xchbinx 301	1 ⊢ (φ ↔ ¬ χ)

Colors of variables: wff setvar class

Syntax hints: ¬ wn 3 ↔ wb 176

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

This theorem depends on definitions: df-bi 177

This theorem is referenced by: 3anor 948 nanbi 1294 2nalexn 1573 ralnex 2624 rexnal 2625 nss 3329 difdif 3392 difab 3523 ssdif0 3609 difin0ss 3616 disjsn 3786 iundif2 4033 iindif2 4035 tfinsuc 4498