ifp1bi - Mathbox for Richard Penner

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Theorem ifp1bi 37847

Description: Substitute the first element of conditional logical operator. (Contributed by RP, 20-Apr-2020.)

**Assertion**
Ref	Expression
ifp1bi	if- if- $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$

**Proof of Theorem ifp1bi**
Step	Hyp	Ref	Expression
1		dfbi2 660	. 2 if- if- if- if- $/\$ if- if-
2		ifpim1g 37846	. . . 4 if- if- $\/$ $/\$ $\/$
3		ancom 466	. . . 4 $\/$ $/\$ $\/$ $\/$ $/\$ $\/$
4	2, 3	bitri 264	. . 3 if- if- $\/$ $/\$ $\/$
5		ifpim1g 37846	. . 3 if- if- $\/$ $/\$ $\/$
6	4, 5	anbi12i 733	. 2 if- if- $/\$ if- if- $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$
7		an42 866	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$
8	1, 6, 7	3bitri 286	1 if- if- $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 196 $\/$ wo 383 $/\$ wa 384 if-wif 1012

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

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ifp 1013

This theorem is referenced by: (None)