ifp1bi - Mathbox for Richard Penner

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Theorem ifp1bi 36140

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 633	. 2 if- if- if- if- $/\$ if- if-
2		ifpim1g 36139	. . . 4 if- if- $\/$ $/\$ $\/$
3		ancom 452	. . . 4 $\/$ $/\$ $\/$ $\/$ $/\$ $\/$
4	2, 3	bitri 253	. . 3 if- if- $\/$ $/\$ $\/$
5		ifpim1g 36139	. . 3 if- if- $\/$ $/\$ $\/$
6	4, 5	anbi12i 702	. 2 if- if- $/\$ if- if- $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$
7		an42 833	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$
8	1, 6, 7	3bitri 275	1 if- if- $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 188 $\/$ wo 370 $/\$ wa 371 if-wif 1424

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 189 df-or 372 df-an 373 df-ifp 1425

This theorem is referenced by: (None)